Magic Graphs:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
2001
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Magic labelings Magic squares are among the more popular mathematical recreations. Their origins are lost in antiquity; over the years, a number of generalizations have been proposed. In the early 1960s, Sedlacek asked whether "magic" ideas could be applied to graphs. Shortly afterward, Kotzig and Rosa formulated the study of graph label ings, or valuations as they were first called. A labeling is a mapping whose domain is some set of graph elements - the set of vertices, for example, or the set of all vertices and edges - whose range was a set of positive integers. Various restrictions can be placed on the mapping. The case that we shall find most interesting is where the domain is the set of all vertices and edges of the graph, and the range consists of positive integers from 1 up to the number of vertices and edges. No repetitions are allowed. In particular, one can ask whether the set of labels associated with any edge - the label on the edge itself, and those on its endpoints - always add up to the same sum. Kotzig and Rosa called such a labeling, and the graph possessing it, magic. To avoid confusion with the ideas of Sedlacek and the many possible variations, we would call it an edge-magic total labeling |
| Beschreibung: | 1 Online-Ressource (XIV, 146 p) |
| ISBN: | 9781461201236 9780817642525 |
| DOI: | 10.1007/978-1-4612-0123-6 |
Internformat
MARC
| LEADER | 00000nmm a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV042419444 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s2001 |||| o||u| ||||||eng d | ||
| 020 | |a 9781461201236 |c Online |9 978-1-4612-0123-6 | ||
| 020 | |a 9780817642525 |c Print |9 978-0-8176-4252-5 | ||
| 024 | 7 | |a 10.1007/978-1-4612-0123-6 |2 doi | |
| 035 | |a (OCoLC)879621241 | ||
| 035 | |a (DE-599)BVBBV042419444 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 511.6 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Wallis, W. D. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Magic Graphs |c by W. D. Wallis |
| 264 | 1 | |a Boston, MA |b Birkhäuser Boston |c 2001 | |
| 300 | |a 1 Online-Ressource (XIV, 146 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 500 | |a Magic labelings Magic squares are among the more popular mathematical recreations. Their origins are lost in antiquity; over the years, a number of generalizations have been proposed. In the early 1960s, Sedlacek asked whether "magic" ideas could be applied to graphs. Shortly afterward, Kotzig and Rosa formulated the study of graph label ings, or valuations as they were first called. A labeling is a mapping whose domain is some set of graph elements - the set of vertices, for example, or the set of all vertices and edges - whose range was a set of positive integers. Various restrictions can be placed on the mapping. The case that we shall find most interesting is where the domain is the set of all vertices and edges of the graph, and the range consists of positive integers from 1 up to the number of vertices and edges. No repetitions are allowed. In particular, one can ask whether the set of labels associated with any edge - the label on the edge itself, and those on its endpoints - always add up to the same sum. Kotzig and Rosa called such a labeling, and the graph possessing it, magic. To avoid confusion with the ideas of Sedlacek and the many possible variations, we would call it an edge-magic total labeling | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Computational complexity | |
| 650 | 4 | |a Combinatorics | |
| 650 | 4 | |a Discrete Mathematics in Computer Science | |
| 650 | 4 | |a Applications of Mathematics | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Graphmarkierung |0 (DE-588)4651657-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Graph |0 (DE-588)4021842-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Graphmarkierung |0 (DE-588)4651657-8 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 689 | 1 | 0 | |a Graph |0 (DE-588)4021842-9 |D s |
| 689 | 1 | |8 2\p |5 DE-604 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-1-4612-0123-6 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027854861 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804153090089156608 |
|---|---|
| any_adam_object | |
| author | Wallis, W. D. |
| author_facet | Wallis, W. D. |
| author_role | aut |
| author_sort | Wallis, W. D. |
| author_variant | w d w wd wdw |
| building | Verbundindex |
| bvnumber | BV042419444 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)879621241 (DE-599)BVBBV042419444 |
| dewey-full | 511.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.6 |
| dewey-search | 511.6 |
| dewey-sort | 3511.6 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-0123-6 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02974nmm a2200517zc 4500</leader><controlfield tag="001">BV042419444</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s2001 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781461201236</subfield><subfield code="c">Online</subfield><subfield code="9">978-1-4612-0123-6</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780817642525</subfield><subfield code="c">Print</subfield><subfield code="9">978-0-8176-4252-5</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-1-4612-0123-6</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)879621241</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042419444</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">511.6</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Wallis, W. D.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Magic Graphs</subfield><subfield code="c">by W. D. Wallis</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Boston, MA</subfield><subfield code="b">Birkhäuser Boston</subfield><subfield code="c">2001</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (XIV, 146 p)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Magic labelings Magic squares are among the more popular mathematical recreations. Their origins are lost in antiquity; over the years, a number of generalizations have been proposed. In the early 1960s, Sedlacek asked whether "magic" ideas could be applied to graphs. Shortly afterward, Kotzig and Rosa formulated the study of graph label ings, or valuations as they were first called. A labeling is a mapping whose domain is some set of graph elements - the set of vertices, for example, or the set of all vertices and edges - whose range was a set of positive integers. Various restrictions can be placed on the mapping. The case that we shall find most interesting is where the domain is the set of all vertices and edges of the graph, and the range consists of positive integers from 1 up to the number of vertices and edges. No repetitions are allowed. In particular, one can ask whether the set of labels associated with any edge - the label on the edge itself, and those on its endpoints - always add up to the same sum. Kotzig and Rosa called such a labeling, and the graph possessing it, magic. To avoid confusion with the ideas of Sedlacek and the many possible variations, we would call it an edge-magic total labeling</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Computational complexity</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Combinatorics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Discrete Mathematics in Computer Science</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Applications of Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Graphmarkierung</subfield><subfield code="0">(DE-588)4651657-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Graph</subfield><subfield code="0">(DE-588)4021842-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Graphmarkierung</subfield><subfield code="0">(DE-588)4651657-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Graph</subfield><subfield code="0">(DE-588)4021842-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-1-4612-0123-6</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027854861</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV042419444 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:04Z |
| institution | BVB |
| isbn | 9781461201236 9780817642525 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027854861 |
| oclc_num | 879621241 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (XIV, 146 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Birkhäuser Boston |
| record_format | marc |
| spelling | Wallis, W. D. Verfasser aut Magic Graphs by W. D. Wallis Boston, MA Birkhäuser Boston 2001 1 Online-Ressource (XIV, 146 p) txt rdacontent c rdamedia cr rdacarrier Magic labelings Magic squares are among the more popular mathematical recreations. Their origins are lost in antiquity; over the years, a number of generalizations have been proposed. In the early 1960s, Sedlacek asked whether "magic" ideas could be applied to graphs. Shortly afterward, Kotzig and Rosa formulated the study of graph label ings, or valuations as they were first called. A labeling is a mapping whose domain is some set of graph elements - the set of vertices, for example, or the set of all vertices and edges - whose range was a set of positive integers. Various restrictions can be placed on the mapping. The case that we shall find most interesting is where the domain is the set of all vertices and edges of the graph, and the range consists of positive integers from 1 up to the number of vertices and edges. No repetitions are allowed. In particular, one can ask whether the set of labels associated with any edge - the label on the edge itself, and those on its endpoints - always add up to the same sum. Kotzig and Rosa called such a labeling, and the graph possessing it, magic. To avoid confusion with the ideas of Sedlacek and the many possible variations, we would call it an edge-magic total labeling Mathematics Computational complexity Combinatorics Discrete Mathematics in Computer Science Applications of Mathematics Mathematik Graphmarkierung (DE-588)4651657-8 gnd rswk-swf Graph (DE-588)4021842-9 gnd rswk-swf Graphmarkierung (DE-588)4651657-8 s 1\p DE-604 Graph (DE-588)4021842-9 s 2\p DE-604 https://doi.org/10.1007/978-1-4612-0123-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Wallis, W. D. Magic Graphs Mathematics Computational complexity Combinatorics Discrete Mathematics in Computer Science Applications of Mathematics Mathematik Graphmarkierung (DE-588)4651657-8 gnd Graph (DE-588)4021842-9 gnd |
| subject_GND | (DE-588)4651657-8 (DE-588)4021842-9 |
| title | Magic Graphs |
| title_auth | Magic Graphs |
| title_exact_search | Magic Graphs |
| title_full | Magic Graphs by W. D. Wallis |
| title_fullStr | Magic Graphs by W. D. Wallis |
| title_full_unstemmed | Magic Graphs by W. D. Wallis |
| title_short | Magic Graphs |
| title_sort | magic graphs |
| topic | Mathematics Computational complexity Combinatorics Discrete Mathematics in Computer Science Applications of Mathematics Mathematik Graphmarkierung (DE-588)4651657-8 gnd Graph (DE-588)4021842-9 gnd |
| topic_facet | Mathematics Computational complexity Combinatorics Discrete Mathematics in Computer Science Applications of Mathematics Mathematik Graphmarkierung Graph |
| url | https://doi.org/10.1007/978-1-4612-0123-6 |
| work_keys_str_mv | AT walliswd magicgraphs |