Partial domination of middle graphs

2025/01/06 by Zhang, Shumin, Li, Minhui, Dong, Fengming
#05C05 #05C12 #05C76 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2501.02879

Abstract

For any graph G=(V,E), a subset S⊆ V is called \it an isolating set of G if V∖ N_G[S] is an independent set of G, where N_G[S]=S∪ N_G(S), and \it the isolation number of G, denoted by ι(G), is the size of a smallest isolating set of G. In this article, we show that the isolation number of the middle graph of G is equal to the size of a smallest maximal matching of G.

Related

• Inequalities between Partial Domination and Independent Partial\n Domination in Graphs
• Partial domination - the isolation number of a graph
• Disjoint Isolating Sets and Graphs with Maximum Isolation Number
• On the number of isolate dominating sets of certain graphs
• On the isolation number of graphs with minimum degree four