Journal Article

Domination and minimal domination polynomial of H—generalized join graphs

S., Manikandan, S.P., Murugan, A, Selvakumar

2025

Overview

Let H be a connected labeled graph. A H—generalized join graph is a graph obtained by H—generalized join operation of family of graphs 𝓖 = {Gv : v ∈ V(H)} constrained by family of vertex subsets 𝒮 = {Sv ⊂ V(Gv ) : v ∈ V(H)}. In this article, we characterize all the dominating sets and the minimal dominating sets of H—generalized join graphs. Consequently, we compute the (multivariate) domination polynomial and the minimal domination polynomial of H—generalized join graphs. We also compute the domination number of H—generalized join graphs. Finally, as an illustration, we calculate the domination polynomial and the minimal domination polynomial of multipartite graphs, the corona product of graphs, Kn —generalized join graphs, and K n 1 , … , n m —generalized join graphs.

• Publisher: University of Nis, Faculty of Sciences and Mathematics