Independent 2-point set domination in graphs with specified girth
Year: 2025
Type: article
Abstract: A set D of vertices in a connected graph G is said to be an independent 2-point set dominating set (or in short i-2psd set) of G if D is an independent set and for every subset S⊆V−D there exists a non-empty subset T⊆D containing at most 2 vertices such that the induced subgraph 〈S∪T〉 is connected. A graph which possesses an i-2psd set is called an i-2psd graph. Every finite graph need not be an i-2psd graph; for instance C7. In this paper we continue to explore graphs which possess an i-2psd set and discuss i-2psd graphs with specified girth. We exhibit a relation between diameter and girth of an i-2psd graph. We characterize extremal i-2psd graphs with maximum girth, and further present a partial characterization of i-2psd graphs with girth 5.
Author: Deepti Jain
Institution: University of Delhi
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,226
OpenAlex ID: W4409813094