The Global Set-Domination Number of a Graph

Sampathkumar, E. and Latha, L.P. (1994) The Global Set-Domination Number of a Graph. Indian Journal of Pure & Applied Mathematics, 25 (10). pp. 1053-1057.

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Let G be a co-connected graph. A set D subset of V is a `set-dominating set' (sd-set) if for every set S subset of V - D, there exists a nonempty set T subset of D such that the subgraph S boolean OR T] is connected. Further, D is a global sd-set if D is an sd-set of both G and ($) over bar G. The `set-domination number' gamma(s) and the `global set-domination number' gamma(sg) of G are defined as expected. Theorem 1 - For a tree of order p with e end vertices, gamma(sg) = p - e. Theorem 2 - If diam G = 3, then gamma(sg) less than or equal to gamma(s)+ 2; if diam G = 4, then gamma sg less than or equal to gamma(s) + 1; if diam G greater than or equal to 5, then gamma(sg) = gamma(s).

Item Type: Article
Subjects: E Mathematical Science > Mathematics
Divisions: Department of > Mathematics
Depositing User: Users 23 not found.
Date Deposited: 02 May 2021 05:05
Last Modified: 02 May 2021 05:05

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