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Defining numbers in some of the Harary graphs

✍ Scribed by D.A. Mojdeh; A.P. Kazemi

Publisher: Elsevier Science
Year: 2009
Tongue: English
Weight: 376 KB
Volume: 22
Category: Article
ISSN: 0893-9659
DOI: 10.1016/j.aml.2008.11.001

No coin nor oath required. For personal study only.

✦ Synopsis

Defining set

The defining number The strong defining number Harary graph a b s t r a c t

In a given graph G = (V , E), a set of vertices S with an assignment of colors to them is said to be a defining set of the vertex coloring of G if there exists a unique extension of the colors of S to a c ≥ χ (G) coloring of the vertices of G. A defining set with minimum cardinality is called a minimum defining set and its cardinality is the defining number. In this note, we study the chromatic number, the defining number and the strong defining number in some of the Harary graphs.

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