Paired domination and 2- distance Paired domination of the flower graph\n f_{n\× m}

2019/07/02 by Tanveer Iqbal, Iqbal, Tanveer, Syed Ahtsham Ul Haq Bokhary +1
Computer Science · #05C15 #05C65 #Advanced Graph Theory Research #Combinatorics (math.CO) #Complexity and Algorithms in Graphs #FOS: Mathematics #Graph Labeling and Dimension Problems

paper · pdf · doi:10.48550/arxiv.1907.01210

openalex publication_date 2019/07/02 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

Let G = (V, E) be a graph without an isolated vertex. A set D\⊆\nV(G) is a k-distance paired domination set of G if D is a k-distance\ndominating set of G and the induced subgraph \⟨ D \⟩ has a\nperfect matching. The minimum cardinality of a k-distance paired dominating\nset for graph G is the k-distance paired domination number, denoted by\n\γ_p ^k(G). In this paper, the k-distance paired domination of the\nflower graph f_{n\× m} is discussed. For m,n\≥ 3, the exact values\nfor paired domination number and 2-distance paired domination number of\nflower graph f_{n\× m} are determined\n

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