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Some results on λ-valuation of graphs involving complete bipartite graphs

✍ Scribed by Sze-Chin Shee

Publisher
Elsevier Science
Year
1991
Tongue
English
Weight
389 KB
Volume
87
Category
Article
ISSN
0012-365X

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✦ Synopsis

Shee, S.-C., Some results on I-valuation of graphs involving complete bipartite graphs, Discrete Mathematics 87 (1991) 73-80.

In this paper we show that a graph G obtained from a complete bipartite graph K,,, and a collection of q (cmax{m, n}) stars G, by joining the centre of G, to every vertex of K,,, and joining the centre of G, to a vertex (not the centre) of G,+, (i = 1, 2, . . . , q -1) is strongly harmonious. We also prove that a graph obtained from a collection of t complete bipartite graphs Km,+, with bipartition (X,, Yi) by joining exactly one member in Y with a member in X,+, (i = 1,2, . , t -1) is strongly c-elegant. The windmill graph K$#'i of n complete bipartite graphs Kz,2 with a common vertex is also shown to be harmonious for all n 2 2.

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