At its most basic level, this book is about dominating sets in graphs. A dominating set of a
graph G is a subset D of vertices having the property that each vertex of G is in D or is …

In this paper, we introduce and do an initial investigation of a variant of Grundy hop
domination in a graph called the connected Grundy hop domination. We show that the …

In this paper, we revisit the concepts of Grundy domination and Grundy hop domination in
graphs and give some realization results involving these parameters. We show that the …

Let G be an undirected graph with vertex and edge sets V (G) and E (G), respectively. Let
S=(v1, v2,···, vk) be a sequence of distinct vertices of G and let Sˆ={v1, v2,..., vk}. Then S is a …

In this paper, we determine the graphs (respectively, trees) with maximum spectral radius
among all graphs (respectively, trees) with zero forcing number at most $ k $. As an …

In this paper, we continue the investigation of different types of (Grundy) dominating
sequences. We consider four different types of Grundy domination numbers and the related …

A unified framework for the Expander Mixing Lemma for irregular graphs using adjacency
eigenvalues is presented, as well as two new versions of it. While the existing Expander …

In this paper, we study a dynamic coloring of the vertices of a graph G that starts with an
initial subset S of colored vertices, with all remaining vertices being uncolored. At each …

This paper presents strong connections between four variants of the zero forcing number
and four variants of the Grundy domination number. These connections bridge the …

Domination game (Brešar et al. in SIAM J Discrete Math 24: 979–991, 2010) and total
domination game (Henning et al. in Graphs Comb 31: 1453–1462 (2015) are by now well …