Advances and Applications in Discrete Mathematics
Volume 20, Issue 1, Pages 111 - 132
(January 2019) http://dx.doi.org/10.17654/ |
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CONNECTED PERFECT HOP DOMINATING SETS UNDER SOME BINARY OPERATIONS
Raicah C. Rakim, Helen M. Rara and Yamilita M. Pabilona
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Abstract: Let be a simple graph. A set is a perfect hop dominating set of G if for every there is exactly one vertex such that The smallest cardinality of a perfect hop dominating set of G is called the perfect hop domination number of G, denoted by A perfect hop dominating set is called a connected perfect hop dominating set of G if the induced subgraph of S is connected. The smallest cardinality of a connected perfect hop dominating set in G is called the connected perfect hop domination number of G and is denoted by In this paper, we characterize the connected perfect hop dominating sets in the join, corona, lexicographic product and Cartesian product of graphs and determine their corresponding connected perfect hop domination number. |
Keywords and phrases: perfect hop domination, connected perfect hop domination, join, corona, lexicographic product, Cartesian product.
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