Connected dom-forcing sets in graphs
Combinatorics
2025-05-19 v1
Abstract
In a graph G, a dominating set Df subset of V (G) is called a dom-forcing set if the sub-graph induced by Df must form a zero forcing set. The minimum cardinality of such a set is known as the dom-forcing number of the graph G, denoted by Fd(G). A connected dom-forcing forcing set of a graph G, is a dom-forcing set of G that induces a sub graph of G which is connected. The connected dom-forcing number of G, Fcd(G), is the minimum size of a connected dom-forcing set. This study delves into the concept of the connected dom-forcing number Fcd(G), examining its properties and characteristics. Furthermore, it seeks to accurately determine Fcd(G) for several well-known graphs and their graph products.
Cite
@article{arxiv.2505.11038,
title = {Connected dom-forcing sets in graphs},
author = {Susanth P and Charles Dominic and Premodkumar K P},
journal= {arXiv preprint arXiv:2505.11038},
year = {2025}
}
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16 pages