# Bounds on the number of isolates in sum graph labeling

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 dc.contributor.author Nagamochi, H. dc.contributor.author Miller, M. dc.contributor.author Slamin dc.date.accessioned 2013-08-22T04:21:23Z dc.date.available 2013-08-22T04:21:23Z dc.date.issued 2001 dc.identifier.issn 0012-365X dc.identifier.uri http://repository.unej.ac.id/handle/123456789/816 dc.description.abstract A simple undirected graph H is called a sum graph if there is a labeling L of the vertices en_US of H into distinct positive integers such that any two vertices u and v of H are adjacent if and only if there is a vertex w with label L(w) = L(u) + L(v). The sum number (G) of a graph G = (V; E) is the least integer r such that the graph H consisting of G and r isolated vertices is a sum graph. It is clear that (G)6|E|. In this paper, we discuss general upper and lower bounds on the sum number. In particular, we prove that, over all graphs G = (V; E) with 5xed |V|¿3 and |E|, the average of (G) is at least |E| − 3|V|(log|V|)=[log(( |V| 2 )=|E|)] − |V| − 1. In other words, for most graphs, (G) ∈ (|E|). dc.language.iso en_US en_US dc.publisher Discrete Mathematics en_US dc.relation.ispartofseries Vol. 240 (2001) pp. 175-185; dc.subject Sum Labelling en_US dc.subject Bound en_US dc.subject isolated vertices en_US dc.title Bounds on the number of isolates in sum graph labeling en_US dc.type Article en_US
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