Consider simple, connected, and undirected graphs where V  and E denote the vertex set and edge set of the graph, respectively. The set \( Y \subseteq V\) is the super dominating set if \( \forall ~ w \in \bar {Y}, \exists ~ x \in Y : N(x)\cap \bar {Y}=\{w\}\) , where \(\bar {Y} =V \setminus Y\) . The super domination number, \(\gamma _{sp}(G)\) is the lowest cardinality among all the super dominating sets in P. The comb product of the graphs P and Q, \(P {\triangleright \circ } Q\) can be generated by selecting a copy of P and \(\vert V(P) \vert \) copies of Q. We analyzed the super domination number of various graph families with a particular emphasis on comb products. This chapter focuses on the super domination number of comb products of graphs and its relationship with other graph parameters.

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Super Domination Number of Cycle Based Graphs and Comb Product of Graphs

  • Anjana T. S.,
  • Silpa Sreekumar,
  • Silpa S.,
  • P. Manjusha

摘要

Consider simple, connected, and undirected graphs where V  and E denote the vertex set and edge set of the graph, respectively. The set \( Y \subseteq V\) is the super dominating set if \( \forall ~ w \in \bar {Y}, \exists ~ x \in Y : N(x)\cap \bar {Y}=\{w\}\) , where \(\bar {Y} =V \setminus Y\) . The super domination number, \(\gamma _{sp}(G)\) is the lowest cardinality among all the super dominating sets in P. The comb product of the graphs P and Q, \(P {\triangleright \circ } Q\) can be generated by selecting a copy of P and \(\vert V(P) \vert \) copies of Q. We analyzed the super domination number of various graph families with a particular emphasis on comb products. This chapter focuses on the super domination number of comb products of graphs and its relationship with other graph parameters.