Bipartite Domination Number of Mycielski Graph of Some Graph Families
Winelyn P. Pelias *
Department of Mathematics, College of Arts and Sciences, Central Mindanao University, Musuan, Maramag, Bukidnon, Philippines.
Isagani S. Cabahug, Jr.
Department of Mathematics, College of Arts and Sciences, Central Mindanao University, Musuan, Maramag, Bukidnon, Philippines.
*Author to whom correspondence should be addressed.
Abstract
For a nontrivial connected graph G, a non-empty set S \(\subseteq\) V (G) is a bipartite dominating set of graph G, if the subgraph G[S] induced by S is bipartite and for every vertex not in S is dominated by any vertex in S. The bipartite domination number denoted by \(\gamma\)bip(G) of graph G is the minimum cardinality of a bipartite dominating set G. In this paper, we determine the exact bipartite domination number of a crown graph and its mycielski graph as well as the bipartite domination number of the mycielski graph of path and cycle graphs.
Keywords: Bipartite dominating set, bipartite domination number