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On felicitous graphs

✍ Scribed by Sin-Min Lee; E. Schmeichel; S.C. Shee

Publisher: Elsevier Science
Year: 1991
Tongue: English
Weight: 684 KB
Volume: 93
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(91)90256-2

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✦ Synopsis

A graph with n edges is called harmonious if it is possible to label the vertices with distinct numbers (modulo n) in such a way that the edge labels which are sums of end-vertex labels are also distinct (modulo n). A ;seneralization of harmonious graphs is felicitous graphs. In felicitous labelling distinct numbers (modulo n + 1) are used to label the vertices of a graph with n edges so that the edge labels are distinct (modulo n). We give some necessary conditions for a graph to be felicitous. Somr families of graphs (cycles of order 4k, complete bipartite graphs, generalized Petersen graphs, . . .) are shown to be felicitous, while others (cycles of order 4k + 2, the complete graph K, when n a 5. . .) are not. We also find that almost all graphs are not felicitous.

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