Dominator coloring of a graph is a proper (vertex) coloring with the property that every vertex
is either alone in its color class or adjacent to all vertices of at least one color class. A …

The concept of vague graph was introduced early by Ramakrishna and substantial graph
parameters on vague graphs were proposed such graph coloring, connectivity, dominating …

A domination coloring of a graph G is a proper vertex coloring of G, such that each vertex of
G dominates at least one color class (possibly its own class), and each color class is …

In this paper, we study two popular variants of Graph Coloring–Dominator Coloring and
Class Domination Coloring. In both problems, we are given a graph G and a ℓ∈ N as input …

Consider a graph G=(V, E) and a function f: V→{0, 1, 2}. A vertex u with f (u)= 0 is defined as
undefended by f if it lacks adjacency to any vertex with a positive f-value. The function f is …

Given a graph G=(V, E), the Perfect Italian domination function is a mapping f: V→{0, 1, 2}
such that for any vertex v∈ V with f (v) equals zero,∑ u∈ N (v) f (u) must be two. In simpler …

Given a graph $ G=(V, E) $, a function $ f: V\to\{0, 1, 2\} $ is said to be a\emph {Roman
Dominating function} if for every $ v\in V $ with $ f (v)= 0$, there exists a vertex $ u\in N (v) …

A strict strong coloring of a graph G is a proper coloring of G in which every vertex of the
graph is adjacent to every vertex of some color class. The minimum number of colors …

A dominator coloring of a graph G is a proper coloring in which every vertex of G dominates
every vertex of at least one-color class possibly its own class and each color class is …

A partition of the vertex set V (G) of a graph G into V (G)= V_1 ∪ V_2 ∪ ⋯ ∪ V_k V (G)= V
1∪ V 2∪⋯∪ V k is called ak-strong subcoloring if d (x, y) ≠ 2 d (x, y)≠ 2 in G for every x, y …