On the total and AVD-total coloring of graphs

Total Game Coloring of Graphs

Total variant of well known graph coloring game is considered. We determine exact values of χ ′′ g for some classes of graphs and show that total game chromatic number is bounded from above by ∆ + 3∆ +. We also show relation between total game coloring number and game coloring index.

On the edge and total GA indices of some graphs

Edge and total coloring of interval graphs

An edge coloring of a graph is a function assigning colors to edges so that incident edges acquire distinct colors. The least number of colors su'cient for an edge coloring of a graph G is called its chromatic index and denoted by ′(G). Let (G) be the maximal degree of G; if ′(G) = (G), then G is said to belong to class 1, and otherwise G is said to belong to class 2. A total coloring of a grap...

Total Coloring of Certain Double Vertex Graphs

In this paper we investigate the total coloring number for double vertex graphs of some of the most common classes of graphs. Mathematics Subject Classification: 05C15

Total coloring of pseudo-outerplanar graphs

A graph is pseudo-outerplanar if each of its blocks has an embedding in the plane so that the vertices lie on a fixed circle and the edges lie inside the disk of this circle with each of them crossing at most one another. In this paper, the total coloring conjecture is completely confirmed for pseudoouterplanar graphs. In particular, it is proved that the total chromatic number of every pseudo-...