On the chromaticity of the 2-degree integral subgraph ofq-trees
A graphG is called to be a 2-degree integral subgraph of aq-tree if it is obtained by deleting an edge e from an integral subgraph that is contained in exactlyq- 1 triangles. An added-vertexq-treeG with n vertices is obtained by taking two verticesu, v (u, v are not adjacent) in a q-treesT withn -1...
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| Veröffentlicht in: | Journal of applied mathematics & computing 2007-09, Vol.25 (1-2), p.155-167 |
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| container_title | Journal of applied mathematics & computing |
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| creator | Li, Xiaodong Liu, Xiangwu |
| description | A graphG is called to be a 2-degree integral subgraph of aq-tree if it is obtained by deleting an edge e from an integral subgraph that is contained in exactlyq- 1 triangles. An added-vertexq-treeG with n vertices is obtained by taking two verticesu, v (u, v are not adjacent) in a q-treesT withn -1 vertices such that their intersection of neighborhoods ofu, v forms a complete graphK ^sub q^, and adding a new vertexx, new edgesxu, xv, xv ^sub 1^,xv ^sub 2^, ...,xv ^sub q- 4^, where {v ^sub 1^,v ^sub 2^,...,v ^sub q^-4} -K ^sub q^. In this paper we prove that a graphG with minimum degree not equal toq -3 and chromatic polynomialP(G;λ) = λ(λ - 1) ... (λ -q +2)(λ -q +1)^sup 3^(λ -q)^sup n- q- 2^ withn ≥ q + 2 has and only has 2-degree integral subgraph of q-tree withn vertices and added-vertex q-tree withn vertices.[PUBLICATION ABSTRACT] |
| doi_str_mv | 10.1007/BF02832344 |
| format | Article |
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An added-vertexq-treeG with n vertices is obtained by taking two verticesu, v (u, v are not adjacent) in a q-treesT withn -1 vertices such that their intersection of neighborhoods ofu, v forms a complete graphK ^sub q^, and adding a new vertexx, new edgesxu, xv, xv ^sub 1^,xv ^sub 2^, ...,xv ^sub q- 4^, where {v ^sub 1^,v ^sub 2^,...,v ^sub q^-4} -K ^sub q^. In this paper we prove that a graphG with minimum degree not equal toq -3 and chromatic polynomialP(G;λ) = λ(λ - 1) ... (λ -q +2)(λ -q +1)^sup 3^(λ -q)^sup n- q- 2^ withn ≥ q + 2 has and only has 2-degree integral subgraph of q-tree withn vertices and added-vertex q-tree withn vertices.[PUBLICATION ABSTRACT]</description><identifier>ISSN: 1598-5865</identifier><identifier>EISSN: 1865-2085</identifier><identifier>DOI: 10.1007/BF02832344</identifier><language>eng</language><publisher>Dordrecht: Springer Nature B.V</publisher><subject>Alloys ; Chromaticity ; Computation ; Integrals ; Intersections ; Mathematical models ; Triangles</subject><ispartof>Journal of applied mathematics & computing, 2007-09, Vol.25 (1-2), p.155-167</ispartof><rights>Korean Society for Computational & Applied Mathematics 2007</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c955-8fa96c9708f8e2489f08642ac136615334407693cf487fa38dab436204ff0c183</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27923,27924</link.rule.ids></links><search><creatorcontrib>Li, Xiaodong</creatorcontrib><creatorcontrib>Liu, Xiangwu</creatorcontrib><title>On the chromaticity of the 2-degree integral subgraph ofq-trees</title><title>Journal of applied mathematics & computing</title><description>A graphG is called to be a 2-degree integral subgraph of aq-tree if it is obtained by deleting an edge e from an integral subgraph that is contained in exactlyq- 1 triangles. 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| subjects | Alloys Chromaticity Computation Integrals Intersections Mathematical models Triangles |
| title | On the chromaticity of the 2-degree integral subgraph ofq-trees |
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