For a graph G, the definitions of doknation number, denoted y(G), and independent domination number, denoted i(G), are given, and the following results are obtained: oorollrrg 1. For any graph G, y(L(G)) = i@(G)), where Z,(G) is the line graph of G. (This $xh!s t.lic rtsult ~(L(T))~i(L(T)), h w ere
The product of the independent domination numbers of a graph and its complement
β Scribed by E.J. Cockayne; O. Favaron; H. Li; G. MacGillivray
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 240 KB
- Volume
- 90
- Category
- Article
- ISSN
- 0012-365X
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## Abstract For a graphb __F__ without isolated vertices, let __M__(__F__; __n__) denote the minimum number of monochromatic copies of __F__ in any 2βcoloring of the edges of __K__~__n__~. Burr and Rosta conjectured that when __F__ has order __t__, size __u__, and __a__ automorphisms. Independent
In this communication the domination number of the cross product of an elementary path with the complement of another path is exactly determined and some inequalities for general cases are deduced. The paper ends with a Vizing-like conjecture relating the domination number of the cross product of G
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