Dom-forcing Sets in Graphs
P Susanth
Department of Mathematics, Pookoya Thangal Memorial Government College, (Affiliated to University of Calicut), Perinthalmanna, Kerala- 679322, India and Department of Mathematics, St.Joseph’s College (Autonomous), Devagiri, Calicut - 673008, Kerala, India.
Charles Dominic
Department of Mathematics, CHRIST (Deemed to be University), Bengaluru-560029, Karnataka, India.
K P Premodkumar *
Department of Mathematics, Govt. College Malappuram, Kerala- 676509, India.
*Author to whom correspondence should be addressed.
Abstract
dominating set Df ⊆ V (G) of vertices in a graph G is called a dom-forcing set if the set Df must form a zero forcing set. The minimum cardinality of such a set is known as the dom-forcing number of the graph G, denoted by Fd(G). This article embarks on an exploration of the dom-forcing number of a graph G. Additionally, it delves into the precise determination of Fd(G) for certain well-known graphs like path, cycle, cocunut tree graph, dimond snake graph, triangualr snake graph, hypercube graph, Petersen graph, pinapple graph, complete graph, complete bipartate graph, wheel graph, helm graph etc. Also investigate dom-forcing number of splitting graph of a graph.
Keywords: Zero forcing number, Domination number, Dom-forcing nu, domination