Tahmasbpour and Borzooei [12] introduced two different approaches corresponding to

chromatic number of a bipolar fuzzy graph.

The concept of locating

chromatic number is a marriage between the partition dimension and coloring of a graph, first introduced by Chartrand et al in 2002 [5].

Then, we provide a formula based on 0-1 integer programming to get

chromatic number in 9-CAA.

If k is the smallest number of colors, the graph is said to be k-chromatic and k is called the

chromatic number of the graph.

This result implies, in Section 5.1, that every graph G has regular-irregular chromatic index at most 6( [log [chi](G)] + 1), where [chi](G) denotes the classic

chromatic number of G.

Keywords: game colouring number, marking game, activation strategy, graph power, forest, game

chromatic numberIn [2] Hadwiger formulated his well-known and deep conjecture linking the

chromatic number z (G ) of a graph G with clique minors.

The following theorem presented by Mohar in [32] will be useful for determining the face

chromatic number of a (4,6)-fullerene on the projective plane.

In this paper, we obtain the adjacent vertex-distinguishing I-total

chromatic number of ladder graph by constructing method.

The 21 selected papers discuss such topics as the dynamic

chromatic number of graphs, Euclidean designs and coherent configurations, the list coloring of graphs with cycles of length divisible by a given integer, the rational independence roots, a theorem on incidence matrices and quasi-random hyper-graphs, characterizing completely regular codes from an algebraic viewpoint, and the proportion of various graphs in graph-designs.

Definition 4 The

chromatic number [gamma](G) of a graph G is the smallest number of colors needed to color the vertices of G so that no two adjacent vertices share the same color, i.e., the smallest value of k possible to obtain a k-coloring [6]

Later chapters deal with graph colorings, with material on vertex colorings and bounds for the

chromatic number, vertex colorings of graphs embedded on surfaces, and a variety of restricted vertex colorings.