A twin edge k-coloring of a graph G is a proper edge coloring of G with the elements of Zk so that the induced vertex coloring in which the color of a vertex v in G is the sum (in Zk) of the colors of the edges incident with v is a proper vertex coloring. The minimum k for which G has a twin edge k-coloring is called the twin chromatic index of G. Among the results presented are formulas for th...

With any (not necessarily proper) edge k-colouring γ : E(G) −→ {1, . . . , k} of a graph G, one can associate a vertex colouring σγ given by σγ(v) = ∑ e∋v γ(e). A neighbour-sumdistinguishing edge k-colouring is an edge colouring whose associated vertex colouring is proper. The neighbour-sum-distinguishing index of a graph G is then the smallest k for which G admits a neighbour-sum-distinguishin...

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.

let g be a (p,q) graph. an injective map f : e(g) → {±1,±2,...,±q} is said to be an edge pair sum labeling if the induced vertex function f*: v (g) → z - {0} defined by f*(v) = σp∈ev f (e) is one-one where ev denotes the set of edges in g that are incident with a vertex 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} according a...

The magnitudes of chromatic and achromatic edge contrast are statistically independent and thus provide independent information, which can be used for object-contour perception. However, it is unclear if and how much object-contour perception benefits from chromatic edge contrast. To address this question, we investigated how well human-marked object contours can be predicted from achromatic an...

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 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....

Let G = (V, E) be a graph and k > 2 an integer. The general chromatic index x;(G) of G is the minimum order of a partition P of E such that for any set F in P every component in the subgraph (F) induced by F has size at most k1. This paper initiates a study of x;(G) and generalizes some known results on chromatic index. The purpose of this paper is to obtain a generalization of chromatic index....