The injective chromatic number χi(G) [5] of a graph G is the minimum number of colors needed to color the vertices of G such that two vertices with a common neighbor are assigned distinct colors. In this paper we define injective chromatic sum and injective strength of a graph and obtain the injective chromatic sum of complete graph, paths, cycles, wheel graph and complete bipartite graph. We a...

A b-coloring is a proper coloring of the vertices of a graph such that each color class has a vertex that is adjacent to a vertex of every other color. The b-chromatic number b(G) of a graph G is the largest k such that G admits a b-coloring with k colors. A graph G is b-chromatic edge critical if for any edge e of G, the b-chromatic number of G − e is less than the b-chromatic number of G. We ...

In our previous demonstrations of chromatic discrimination in infants, we have used test and surround fields of different chromaticities that abutted each other at sharp chromatic edges. In order to see whether sharp chromatic edges are necessary for infants to make chromatic discriminations, 16-week-old infants were tested with three stimulus configurations in which sharp chromatic edges were ...

The chromatic sum of a graph is introduced in the dissertation of Ewa Kubicka. It is the smallest possible total among all proper colorings of G using natural numbers. In this article we determine tight bounds on the chromatic sum of a connected graph with e edges, 1. THE CHROMATIC SUM A proper coloring of the vertices of the graph G must assign different colors to adjacent vertices. The chroma...

In 2006, Suzuki, and Akbari & Alipour independently presented a necessary and sufficient condition for edge-colored graphs to have a heterochromatic spanning tree, where a heterochromatic spanning tree is a spanning tree whose edges have distinct colors. In this paper, we propose f -chromatic graphs as a generalization of heterochromatic graphs. An edge-colored graph is f -chromatic if each col...

In this paper, we study a new coloring parameter of graphs called the gap vertexdistinguishing edge coloring. It consists in an edge-coloring of a graph G which induces a vertex distinguishing labeling of G such that the label of each vertex is given by the difference between the highest and the lowest colors of its adjacent edges. The minimum number of colors required for a gap vertex-distingu...

Spatial resolution for color is poor, and reports that V1 simple cell respond to oriented achromatic stimuli have led to the view of two independent processing streams, a high-resolution achromatic form system and a low-resolution unoriented color surface system. Recent data have challenged this view, showing that V1 simple cells respond also to oriented chromatic stimuli [5, 7] and that color ...

We study the relationships between the resolving edge chromatic number and other graphical parameters and provide bounds for the resolving edge chromatic number of a connected graph.

We prove several results about three families of graphs. For queen graphs, defined from the usual moves of a chess queen, we find the edge-chromatic number in almost all cases. In the unproved case, we have a conjecture supported by a vast amount of computation, which involved the development of a new edge-coloring algorithm. The conjecture is that the edge-chromatic number is the maximum degre...