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The cordiality of one-point union of n copies of a graph

✍ Scribed by Sze-Chin Shee; Yong-Song Ho

Publisher: Elsevier Science
Year: 1993
Tongue: English
Weight: 877 KB
Volume: 117
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)90337-s

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✦ Synopsis

Shee, S.-C. and Y.-S. Ho, The cordiality of one-point union of n copies of a graph, Discrete Mathematics 117 (1993) 225-243.

In this paper we give an equivalent definition of a cordial graph. The definition implies a previous result of Cahit (1986); it also enables us to find infinite families of noncordial graphs, derive some bound on the number of edges in a cordial graph and establish a necessary and sufficient condition for a one-point union of two n-cliques.

Let G be a rooted graph. We denote by G'"' the graph obtained from n copies of G by identifying their roots. A sufficient condition for G'"' to be cordial is related to the solution of a system involving one equation and two inequalities with their coefficients depending on some binary labellings of G. According to the solvability of the system, we are able to establish a number of necessary and sufficient conditions for the cordiality of G'"' for certain classes of G, such as cycles, complete graphs, wheels, fans and flags. lc4f)l< 1 and IB(f)l d 1.

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