Isolation Number of Transition Graphs

Abstract

Let G=(V,E) be a graph and F be a family of graphs; a subset (S⊆V(G)) is said to be an F-isolating set if G[V(G)∖NG[S]] does not contain F as a subgraph for all F∈F. The F-isolation number of G is the minimum cardinality of an F-isolating set (S) of G, denoted by ι(G,F). When F={K1,k+1}, we use ιk(G) to define the F-isolation number (ι(G,F)). In particular, when k=0, we use the short form of ι(G) instead of ι0(G). A subset (S⊆V(G)) is called an isolating set if V(G)∖NG[S] is an independent set of G. The isolation number of G is the minimum cardinality of an isolating set, denoted by ι(G). In this paper, we mainly focus on research on the isolation number and F-isolation number of a B(G) graph, total graph and central graph of graph G.

Keywords

• partial domination
• isolation number
• bipartite graph
• total graph
• central graph