Geodesic
Injective edge coloring of graphs
Filomat, Tome 33 (2019) no. 19, p. 6411

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DOI

Three edges e1, e2 and e3 in a graph G are consecutive if they form a path (in this order) or a cycle of lengths three. An injective edge coloring of a graph G = (V,E) is a coloring c of the edges of G such that if e1, e2 and e3 are consecutive edges in G, then c(e1) , c(e3). 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
DOI : 10.2298/FIL1919411C
Classification : 05C15
Keywords: Injective coloring, injective edge coloring 
Domingos M Cardoso; J Orestes Cerdeira; Charles Dominic; J Pedro Cruz. Injective edge coloring of graphs. Filomat, Tome 33 (2019) no. 19, p. 6411 . doi: 10.2298/FIL1919411C
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     title = {Injective edge coloring of graphs},
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     year = {2019},
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     doi = {10.2298/FIL1919411C},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL1919411C/}
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