Geodesic
Injective edge coloring of product graphs and some complexity results
Filomat, Tome 37 (2023) no. 12, p. 3963

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

DOI

Three edges e 1 , e 2 and e 3 in a graph G are consecutive if they form a cycle of length 3 or a path in this order. A k-injective edge coloring of a graph G is an edge coloring of G, (not necessarily proper), such that if edges e 1 , e 2 , e 3 are consecutive, then e 1 and e 3 receive distinct colors. The minimum k for which G has a k-injective edge coloring is called the injective edge chromatic index, denoted by χ ′ i (G) [4]. In this article, the injective edge chromatic index of the resultant graphs by the operations union, join, Cartesian product and corona product of G and H are determined, where G and H are different classes of graphs. Also for any two arbitrary graphs G and H, bounds for χ ′ i (G + H) and χ ′ i (G H) are obtained. Moreover the injective edge coloring problem restricted to (2, 3, r)-triregular graph, (2, 4, r)-triregular graph and (2, r)-biregular graph, r ≥ 3 are also been demonstrated to be NP-complete.
DOI : 10.2298/FIL2312963K
Classification : 05C15, 05C76, 03D15
Keywords: injective edge chromatic index, union, join, Cartesian product, corona, complexity, triregular graphs 
Bhanupriya C Ka; Charles Dominic; Sunitha M Sa. Injective edge coloring of product graphs and some complexity results. Filomat, Tome 37 (2023) no. 12, p. 3963 . doi: 10.2298/FIL2312963K
@article{10_2298_FIL2312963K,
     author = {Bhanupriya C Ka and Charles Dominic and Sunitha M Sa},
     title = {Injective edge coloring of product graphs and some complexity results},
     journal = {Filomat},
     pages = {3963 },
     year = {2023},
     volume = {37},
     number = {12},
     doi = {10.2298/FIL2312963K},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2312963K/}
}
TY  - JOUR
AU  - Bhanupriya C Ka
AU  - Charles Dominic
AU  - Sunitha M Sa
TI  - Injective edge coloring of product graphs and some complexity results
JO  - Filomat
PY  - 2023
SP  - 3963 
VL  - 37
IS  - 12
UR  - http://geodesic.mathdoc.fr/articles/10.2298/FIL2312963K/
DO  - 10.2298/FIL2312963K
LA  - en
ID  - 10_2298_FIL2312963K
ER  - 
%0 Journal Article
%A Bhanupriya C Ka
%A Charles Dominic
%A Sunitha M Sa
%T Injective edge coloring of product graphs and some complexity results
%J Filomat
%D 2023
%P 3963 
%V 37
%N 12
%U http://geodesic.mathdoc.fr/articles/10.2298/FIL2312963K/
%R 10.2298/FIL2312963K
%G en
%F 10_2298_FIL2312963K

Cité par Sources :