On the Relation Between the Domination Number and Edge Domination Number of Trees and Claw-Free Cubic Graphs

Zhuo Pan (), Peng Pan and Chongshan Tie
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Zhuo Pan: School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070, China
Peng Pan: Gansu Key Laboratory of Applied Mathematics and Complex Systems, School of Mathematics and Statistics, Lanzhou University, Lanzhou 730030, China
Chongshan Tie: School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070, China

Mathematics, 2025, vol. 13, issue 3, 1-14

Abstract: For a connected graph G = ( V , E ) , the dominating set in graph G is a subset of vertices F ⊂ V such that every vertex of V − F is adjacent to at least one vertex of F . The minimum cardinality of a dominating set of G , denoted by γ ( G ) , is the domination number of G . The edge dominating set in graph G is a subset of edges S ⊂ E such that every edge of E − S is adjacent to at least one edge of S . The minimum cardinality of an edge dominating set of G , denoted by γ ′ ( G ) , is the edge domination number of G . In this paper, we characterize all trees and claw-free cubic graphs with equal domination and edge domination numbers, respectively.

Keywords: domination number; edge domination number; trees; claw-free cubic graphs (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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