TY - JOUR

T1 - On integral sum graphs with a saturated vertex

AU - Chen, Zhibo

N1 - Copyright:
Copyright 2010 Elsevier B.V., All rights reserved.

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

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U2 - 10.1007/s10587-010-0061-z

DO - 10.1007/s10587-010-0061-z

M3 - Article

AN - SCOPUS:77955257003

VL - 60

SP - 669

EP - 674

JO - Czechoslovak Mathematical Journal

JF - Czechoslovak Mathematical Journal

SN - 0011-4642

IS - 3

ER -