1-Factor Forcing in Certain Interconnection Networks
J. Anitha, Indra Rajasingh · Procedia Computer Science · 2020
A effective coloring of the vertices of a graph G starts with an initial subset S of colored vertices, with all residual vertices being uncolored. At each various time interval, a colored vertex with exactly one uncolored adjacent vertex forces this uncolored vertex to be colored. The initial set S is called a forcing set (zero forcing set) of G if, by iteratively applying the forcing process, every vertex in G becomes colored. If the set S has the added property that the subgraph induced by S is a perfect matching or 1-factor, then S is called a 1-factor forcing set of G . The 1-factor forcing number of G denoted ζ P2 (G), is the minimum cardinality of a 1-factor forcing set of G . In this paper, we introduce this new parameter namely the 1-factor forcing number and obtain the same for certain interconnection networks.