The purpose of this survey is to bring some order into the growing literature on a type of
graphs which emerged in the past couple of decades under a wealth of names and in …

The b-chromatic number of a graph G is the largest integer k such that G admits a proper k-
coloring in which every color class contains at least one vertex that has a neighbor in each …

A graph's b-coloring admits proper coloring and has the extra characteristic of having a
dominating node in each color-class in the graph. φ (G), the b-chromatic number, is the …

In this work, we study the δ-chromatic number of a graph, which is the chromatic number of
the δ-complement of a graph. We give a structure of the δ-complements and sharp bounds …

Let G and H be two graphs, each one of them being a path, a cycle or a star. In this paper,
we determine the b-chromatic number of every subdivision-vertex neighbourhood corona …

A b-coloring of a graph is a proper coloring such that every color class contains a vertex
adjacent to at least one vertex in each of the other color classes. The b-chromatic number of …

We consider the b-chromatic number of cartesian products of graphs. We show that the b-
chromatic number of K n□ d for d≥ 3 is one more than the degree; for d≥ 12 this follows …

A b-coloring of a graph G with k colors is a proper coloring of G using k colors in which each
color class contains a color dominating vertex, that is, a vertex which has a neighbor in each …

In this article, we examine the Johan colouring number, Modified Johan colouring number of
Sunlet graph, Johan colouring number of Crown graph, Johan colouring number of Barbell …

In this paper, the b-coloring problem is solved for every subdivision-edge neighborhood
corona of paths, cycles, stars and complete graphs. In addition, some exact values and …