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arXiv · 1510.02626

Injective Edge Chromatic Index of a Graph

Domingos M. Cardoso·J. Orestes Cerdeira·J. Pedro Cruz·Charles Dominic
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Abstract

Three edges $e_{1}, e_{2}$ and $e_{3}$ in a graph $G$ are consecutive if they form a path (in this order) or a cycle of length three. An injective edge coloring of a graph $G = (V,E)$ is a coloring $c$ of the edges of $G$ such that if $e_{1}, e_{2}$ and $e_{3}$ are consecutive edges in $G$, then $c(e_{1})\neq c(e_3)$. The injective edge coloring number $χ_{i}^{'}(G)$ is the minimum number of colors permitted in such a coloring. In this paper, exact values of $χ_{i}^{'}(G)$ for several classes of graphs are obtained, upper and lower bounds for $χ_{i}^{'}(G)$ are introduced and it is proven that checking whether $χ_{i}^{'}(G)= k$ is NP-complete.

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Domingos M. Cardoso, J. Orestes Cerdeira, J. Pedro Cruz, Charles Dominic. 2015-10-09. Injective Edge Chromatic Index of a Graph. https://arxiv.org/abs/1510.02626

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