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A subset \(C\subseteq V(G)\) of a graph G is \(P_3\) -convex if no vertex in \(V (G) \setminus C\) has two neighbors in C. C is said to be \(P_3\) -convex dominating if it is \(P_3\) -convex and dominating. The \(P_3\) -convex domination number \(\gamma _{P_3-con} (G)\) is the cardinality of a minimum \(P_3\) -convex dominating set. We present a necessary condition for achieving the maximum \(P_3\) -convex domination number and identify several graph classes that meet this bound. Additionally, we determine the exact \(P_3\) -convex domination number of generalized Petersen graph P(n, 1).

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\(P_3\) -Convex Domination Number of a Graph

  • 会议论文

  • 发表日期：

    2026年

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  • Anjan Gautam,
  • Biswajit Deb,
  • Puran Dangal

摘要

A subset \(C\subseteq V(G)\) of a graph G is \(P_3\) -convex if no vertex in \(V (G) \setminus C\) has two neighbors in C. C is said to be \(P_3\) -convex dominating if it is \(P_3\) -convex and dominating. The \(P_3\) -convex domination number \(\gamma _{P_3-con} (G)\) is the cardinality of a minimum \(P_3\) -convex dominating set. We present a necessary condition for achieving the maximum \(P_3\) -convex domination number and identify several graph classes that meet this bound. Additionally, we determine the exact \(P_3\) -convex domination number of generalized Petersen graph P(n, 1).