On the power domination number of the Cartesian product of graphs

Abstract

We give a brief survey about the existing results on the power domination of the Cartesian product of graphs, and improve two of the results by determining the exact power domination numbers of two families of graphs, namely, the cylinder P n □ C m and the tori C n □ C m. We also establish the power domination number for K n □ K 1,m , the Cartesian product of a complete graph and a star. c

Penerapan Teori Bilangan Dominasi Jarak Dua Pada Pemilihan Lokasi Pangkal Ojek Online

“…Topik dominasi dalam teori graf mengalami banyak perkembangan. Terdapat berbagai jenis dimoniasi yang menarik untuk diteliti, diantaranya dominasi terhubung (connected domination) [10], dominasi total (total domination) [11], power domination [12], dan lain sebagainya yang dapat dilihat pada [13]. Sejalan dengan topik dominasi, dalam artikel ini diteliti bilangan dominasi jarak dua pada graf bipartit lengkap (Complete Bipartite Graph) dan graf tripartit lengkap (Complete Tripartite Graph) yang dioperasikan secara shackle titik dan shackle sisi.…”

Connected power domination number of product graphs

“…Further, some upper bound for the power domination number of graphs is obtained in [23]. Furthermore, the power domination number of some standard families of graphs and product graphs are studied in [5,6,8,9,14,15,[17][18][19][20][21][22]. Recently, Brimkvo et al [7] introduced the concept of connected power domination number of graph and obtained the exact value for trees, block graph, and cactus graph.…”

Recent Results on the Power Domination Numbers of Graph Products

“…Koh and Soh [7] extended the study of the power domination problem to the Cartesian product of any two of the following graphs: P n , C n , K n , W n and K 1,n . The study was completed in a subsequent paper and all the 15 exact formulas are summarized in [8].…”