The notion of the b-chromatic number of a graph attracted much research interests and recently a new concept, namely the b-chromatic sum of a graph, denoted by (G), has also been introduced. Motivated by the studies on b-chromatic sum of graphs, in this paper we introduce certain new parameters such as -chromatic sum, -chromatic sum, b-chromatic sum, -chromatic sum and -chromatic sum of graphs....

An injective map f : E(G) → {±1, ±2, · · · , ±q} is said to be an edge pair sum labeling of a graph G(p, q) if the induced vertex function f*: V (G) → Z − {0} defined by f*(v) = (Sigma e∈Ev) f (e) is one-one, where Ev denotes the set of edges in G that are incident with a vetex v and f*(V (G)) is either of the form {±k1, ±k2, · · · , ±kp/2} or {±k1, ±k2, · · · , ±k(p−1)/2} U {k(p+1)/2} accordin...

On Sum Coloring of Graphs Mohammadreza Salavatipour Master of Science Graduate Department of Computer Science University of Toronto 2000 The sum coloring problem asks to nd a vertex coloring of a given graph G, using natural numbers, such that the total sum of the colors of vertices is minimized amongst all proper vertex colorings of G. This minimum total sum is the chromatic sum of the graph, ...

The edge strength s(G) of a multigraph G is the minimum number of colors in a minimum sum edge coloring of G. We give closed formulas for the edge strength of bipartite multigraphs and multicycles. These are shown to be classes of multigraphs for which the edge strength is always equal to the chromatic index.

Chromatic number, chromatic sum and chromatic sum number are important graph coloring characteristics. The paper proves that a parallel metaheuristic like the parallel genetic algorithm (PGA) can be efficiently used for computing approximate sum colorings and finding upper bounds for chromatic sums and chromatic sum numbers for hard– to–color graphs. Suboptimal sum coloring with PGA gives usual...

Whitney’s Broken-cycle Theorem states the chromatic polynomial of a graph as a sum over special edge subsets. We give a definition of cycles in hypergraphs that preserves the statement of the theorem there.

The chromatic sum of a graph is the smallest sum of colors among all proper colorings with natural numbers. The strength of a graph is the minimum number of colors necessary to obtain its chromatic sum. A natural generalization of chromatic sum is optimum cost chromatic partition (OCCP) problem, where the costs of colors can be arbitrary positive numbers. Existing results about chromatic sum, s...

We study edge-sum distinguishing labeling, a type of labeling recently introduced by Z. Tuza (2017) in context games. An ESD an $n$-vertex graph $G$ is injective mapping integers $1$ to $l$ its vertices such that for every edge, the sum on endpoints unique. If $ l$ equals $n$, we speak about canonical labeling. focus primarily structural properties this and show several classes graphs if they h...