Isolation Number of Transition Graphs

Junhao Qu and Shumin Zhang ()
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Junhao Qu: School of Mathematics and Statistics, Qinghai Normal University, Xining 810001, China
Shumin Zhang: School of Mathematics and Statistics, Qinghai Normal University, Xining 810001, China

Mathematics, 2024, vol. 13, issue 1, 1-10

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 ) ∖ N G [ 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 = { K 1 , k + 1 } , we use ι k ( 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 ι 0 ( G ) . A subset ( S ⊆ V ( G ) ) is called an isolating set if V ( G ) ∖ N G [ 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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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