Edge and total coloring of interval 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...

Edge-coloring Vertex-weightings of Graphs

Let $G=(V(G),E(G))$ be a simple, finite and undirected graph of order $n$. A $k$-vertex weightings of a graph $G$ is a mapping $w: V(G) to {1, ldots, k}$. A $k$-vertex weighting induces an edge labeling $f_w: E(G) to N$ such that $f_w(uv)=w(u)+w(v)$. Such a labeling is called an {it edge-coloring k-vertex weightings} if $f_{w}(e)not= f_{w}(echr(chr(chr('39')39chr('39'))39chr(chr('39')39chr('39'...

Sub-coloring and Hypo-coloring Interval Graphs

In this paper, we study the sub-coloring and hypo-coloring problems on interval graphs. These problems have applications in job scheduling and distributed computing and can be used as “subroutines” for other combinatorial optimization problems. In the sub-coloring problem, given a graph G, we want to partition the vertices of G into minimum number of sub-color classes, where each sub-color clas...

On the edge and total GA indices of some graphs

Edge Coloring by Total Labelings of 4-regular Circulant Graphs

Edge-coloring total k-labeling of a connected graph G is an assignment f of non negative integers to the vertices and edges of G such that two adjacent edges e = uv and e = uv of G have different weights. The weight of an edge uv is defined by: w(e = uv) = f(u) + f(v) + f(e). In this paper, we study the chromatic number of the edge coloring by total labeling of 4-regular circulant graphs Cn(1, k).