Domination parameters of the splitting graph of a graph

Document Type : Original paper

Authors

1 Department of Mathematics, Madurai Kamaraj University, Madurai, Tamilnadu, India

2 Department of Mathematics, The Madura College, Madurai, Tamilnadu, India

3 Birla Institute of Technology and Sciences Pilani, Dubai Campus

4 Director (n-CARDMATH) Kalasalingam University Anand Nagar, Krishnankoil-626 126 Tamil Nadu, India

Abstract

Let $G=(V,E)$ be a graph of order $n$ and size $m.$ The graph $Sp(G)$ obtained from $G$ by adding a new vertex $v'$ for every vertex $v\in V$ and joining $v'$ to all neighbors of $v$ in $G$ is called the splitting graph of $G.$ In this paper, we determine the domination number, the total domination number, connected domination number, paired domination number and independent domination number for the splitting graph $Sp(G).$

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References

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Communications in Combinatorics and Optimization
Volume 8, Issue 4
December 2023
Pages 631-637

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