Bounds on the number of isolates in sum graph labeling

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Show simple item record Nagamochi, H. Miller, M. Slamin 2013-08-22T04:21:23Z 2013-08-22T04:21:23Z 2001
dc.identifier.issn 0012-365X
dc.description.abstract A simple undirected graph H is called a sum graph if there is a labeling L of the vertices 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|). en_US
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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    Abstract artikel jurnal yang dihasilkan oleh staf Unej (fulltext bagi yg open access)

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