Injective Edge Chromatic Index of a Graph
Domingos M. Cardoso, J. Orestes Cerdeira, J. Pedro Cruz, Charles, Dominic

TL;DR
This paper introduces the concept of the injective edge chromatic index, provides exact values and bounds for various graph classes, and proves the NP-completeness of determining this index.
Contribution
It defines the injective edge coloring number, computes it for several graph classes, and establishes its computational complexity as NP-complete.
Findings
Exact values of $ ext{chi}_i'(G)$ for specific graph classes
Upper and lower bounds for $ ext{chi}_i'(G)$
NP-completeness of deciding $ ext{chi}_i'(G)=k$
Abstract
Three edges and in a graph are consecutive if they form a path (in this order) or a cycle of length three. An injective edge coloring of a graph is a coloring of the edges of such that if and are consecutive edges in , then . The injective edge coloring number is the minimum number of colors permitted in such a coloring. In this paper, exact values of for several classes of graphs are obtained, upper and lower bounds for are introduced and it is proven that checking whether is NP-complete.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · Limits and Structures in Graph Theory
