Advances and Applications in Discrete Mathematics
Volume 20, Issue 1, Pages 25 - 36
(January 2019) http://dx.doi.org/10.17654/ |
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OUTER-CONNECTED 2-DOMINATING SETS OF GRAPHS
Sergio R. Canoy, Jr. and Bernadette D. Domoloan
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Abstract: Let be a simple graph. A subset S of is an outer-connected 2-dominating set of G if S is a 2-dominating set of G and the graph is connected. The outer-connected 2‑domination number of G, denoted by is the smallest cardinality of an outer-connected 2-dominating set of G. In this paper, we characterize the outer-connected 2-dominating sets of the join, corona, and lexicographic product of graphs. As direct consequences, the corresponding bounds or exact values of the outer-connected 2-domination numbers of these graphs are obtained. |
Keywords and phrases: 2-domination, outer-connected, join, corona, lexicographic product.
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