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Domination alteration sets in graphs

✍ Scribed by Douglas Bauer; Frank Harary; Juhani Nieminen; Charles L. Suffel

Book ID: 103058368
Publisher: Elsevier Science
Year: 1983
Tongue: English
Weight: 738 KB
Volume: 47
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(83)90085-7

No coin nor oath required. For personal study only.

✦ Synopsis

The domination number a(G) of a graph G is the size of a minimum dominating set, i.e., a set of points with the property that every other point is adjacent to a point of the set. In general a(G) can be made to increase or decrease by the removal of points from G. Our main objective is the study of this phenomenon.

For example we show that if T is a tree with at least three points then a(T -u) > a(T) if and only if u is in every minimum dominating set of 7'. Removal of a set of lines from a graph G cannot decrease the domination number. We obtain some upper bounds on the size of a minimum set of lines which when removed from G increases the domination number.

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