Advances and Applications in Discrete Mathematics
Volume 24, Issue 2, Pages 117 - 128
(July 2020) http://dx.doi.org/10.17654/DM024020117 |
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DUAL-PERFECT DOMINATION IN GRAPHS
Romar B. Dinoy and Emiliano C. Maravilla
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Abstract: A subset S of in a graph G is said to be a dual-perfect dominating set if every vertex is adjacent to exactly two vertices in S. The dual-perfect domination number of G, denoted by is the smallest cardinality of the dual-perfect dominating set of G. Any dual-perfect dominating set of G of cardinality is then referred to as a -set of G. This study focuses mainly on the dual-perfect domination in graphs. Specifically, this study is geared to generate results out of the following objectives: (a) to characterize the dual-perfect dominating sets on some graphs; and (b) to determine exact values or bounds of the dual-perfect domination numbers of the join and corona of graphs. |
Keywords and phrases: domination, dual-perfect, perfect, join, corona.
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