Bounds of point-set domination number

Document Type : Short notes

Authors

1 Department of Mathematics, University of Delhi, Delhi-110007, India

2 Department of Mathematics, Deshbandhu College, University of Delhi, Delhi-110007, India

3 Department of Mathematics, Sri Venkateswara College, University of Delhi, Delhi-110021, India

Abstract

A subset $D$ of the vertex set $V(G)$ in a graph $G$ is a point-set dominating set (or, in short, psd-set) of $G$ if for every set $S\subseteq V- D$, there exists a vertex $v\in D$ such that the induced subgraph $\langle S\cup \{v\}\rangle$ is connected.  The minimum cardinality of a psd-set of $G$ is called the point-set domination number of $G$. In this paper, we establish two sharp lower bounds for point-set domination number of a graph in terms of its diameter and girth. We characterize graphs for which lower bound of point set domination number is attained in terms of its diameter. We also establish an upper bound and give some classes of graphs which attains the upper bound of point set domination number.

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References

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Communications in Combinatorics and Optimization
Volume 9, Issue 1
March 2024
Pages 79-87

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