the chromatic number of a graph g, denoted by χ(g), is the minimum number of colors such that g can be colored with these colors in such a way that no two adjacent vertices have the same color. a clique in a graph is a set of mutually adjacent vertices. the maximum size of a clique in a graph g is called the clique number of g. the turán graph tn(k) is a complete k-partite graph whose partition...

The local antimagic total vertex labeling of graph G is a that every vertices and edges label by natural number from 1 to such two adjacent has different weights, where sum the labels all incident vertex. If start smallest then edge so kind coloring called super labeling. That induces for v, weight w(v) color v. minimum colors obtained chromatic G, denoted χlsat(G). In this paper, we consider G...

A skew edge coloring of a graph G is defined to be a set of two edge colorings such that no two edges are assigned the same unordered pair of colors. The skew chromatic index s(G) is the minimum number of colors required for a skew edge coloring of G. In this paper, skew edge coloring of certain classes of graphs are determined. Furthermore, the skew chromatic index of those graphs is obtained ...

The chromatic sum Σ(G) of a graph G is the smallest sum of colors among of proper coloring with the natural number. In this paper, we introduce a necessary condition for the existence of graph homomorphisms. Also, we present Σ(G) < χf (G)|G| for every graph G.

The adaptable chromatic number of a graph G is the smallest integer k such that for any edge k-colouring of G there exists a vertex kcolouring of G in which the same colour never appears on an edge and both its endpoints. (Neither the edge nor the vertex colourings are necessarily proper in the usual sense.) We give an efficient characterization of graphs with adaptable chromatic number at most...

A strong edge coloring of a graph is a proper edge coloring in which every color class is an induced matching. The strong chromatic index of a graph is the minimum number of colors needed to obtain a strong edge coloring. In an analogous way, we can define the list version of strong edge coloring and list version of strong chromatic index. In this paper we prove that if G is a graph with maximu...

An outer-1-planar graph is a admitting drawing in the plane so that all vertices appear outer region of and every edge crosses at most one other edge. This paper establishes local structure graphs by proving each contains seventeen fixed configurations, list those configurations minimal sense for configuration there exist containing this do not contain any another sixteen configurations. There ...

Abstract. A skew edge coloring of a graph G is defined to be a set of two edge colorings such that no two edges are assigned the same unordered pair of colors. The skew chromatic index s(G) is the minimum number of colors required for a skew edge coloring of G. In this paper, an algorithm is determined for skew edge coloring of circular ladder graphs. Alsothe skew chromatic index of circular la...