WebA k -injective edge coloring of a graph G is a coloring f: E ( G) → C = { 1, 2, 3, …, k }, such that if e 1, e 2 and e 3 are consecutive edges in G, then f ( e 1) ≠ f ( e 3). χ i ′ ( G) = min { k G has a k -injective edge coloring } is called the injective edge coloring number.

Note on injective edge-coloring of graphs - ScienceDirect

WebEquivalently, suppose we color the edges of \(\Sigma\) red, green, or blue in arbitrary order so that (1) every cycle contains at least one blue edge, (2) every edge cut contains at least one red edge, and (3) an edge is green if and only if it cannot be colored either red or blue. Then the red, green, and blue edges respectively define the ... WebAn injective edge-coloring c of a graph G is an edge-coloring such that if e 1, e 2, and e 3 are three consecutive edges in G (they are consecutive if they form a path or a cycle of … on which day could labor day fall

Injective edge-coloring of graphs with given maximum …

WebAn injective k -edge coloring of a graph G = ( V ( G), E ( G)) is a k -edge coloring φ such that if e 1 and e 2 are at distance exactly 2 or in the same triangle, then φ ( e 1) ≠ φ ( e 2). The injective chromatic index of G, denoted by χ i ′ ( G), is the minimum k such that G has an injective k -edge coloring. The edge weight of G is ... WebJul 15, 2024 · An injective coloring of a graph is a vertex coloring such that any pair of vertices having a common neighbor receives distinct colors. Panda and Priyamvada [ 12 ] proved complexity results for some subclasses of bipartite graphs, which can be re-interpreted as results on exact square coloring. WebMay 19, 2024 · The minimum k for which G has a k -injective edge coloring is called the i n j e c t i v e e d g e c o l o r i n g n u m b e r, denoted by χ i ′ ( G). In this paper, we consider … on which date mother day