Dominion of some graphs
Combinatorics
2026-01-01 v1 Discrete Mathematics
Abstract
Given a graph G equals (V,E), a subset S subset of V is a dominating set if every vertex in V minus S is adjacent to some vertex in S. The dominating set with the least cardinality, gamma, is called a gamma-set which is commonly known as a minimum dominating set. The dominion of a graph G, denoted by zeta(G), is the number of its gamma-sets. Some relations between these two seemingly distinct parameters are established. In particular, we present the dominions of paths, some cycles and the join of any two graphs.
Cite
@article{arxiv.2512.24115,
title = {Dominion of some graphs},
author = {Julian Allagan and Benkam Bobga},
journal= {arXiv preprint arXiv:2512.24115},
year = {2026}
}
Comments
12 pages, 1 figure