On integral sum graphs with a saturated vertex

Zhibo Chen

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

As introduced by F. Harary in 1994, a graph G is said to be an integral sum graph if its vertices can be given a labeling f with distinct integers so that for any two distinct vertices u and v of G, uv is an edge of G if and only if f(u)+f(v) = f(w) for some vertex w in G. We prove that every integral sum graph with a saturated vertex, except the complete graph K3, has edge-chromatic number equal to its maximum degree. (A vertex of a graph G is said to be saturated if it is adjacent to every other vertex of G.) Some direct corollaries are also presented.

Original languageEnglish (US)
Pages (from-to)669-674
Number of pages6
JournalCzechoslovak Mathematical Journal
Volume60
Issue number3
DOIs
StatePublished - Aug 10 2010

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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