Integral Sum Numbers of Graphs

Sheng Chyang Liaw, David Kuo, Gerard J. Chang

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

Abstract

The sum graph of a set S of positive integers is the graph G+(S) having S as its vertex set, with two distinct vertices adjacent whenever their sum is in S. If S is allowed to be a subset of all integers, a graph so obtained is called an integral sum graph. The integral sum number of a given graph G is the smallest number of isolated vertices which when added to G result in an integral sum graph. In this paper, we find the integral sum numbers of caterpillars, cycles, wheels, and complete bipartite graphs.

Original languageEnglish
Pages (from-to)259-268
Number of pages10
JournalArs Combinatoria
Volume54
StatePublished - Jan 2000

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