Injective edge coloring of product graphs and some complexity results
- Title
- Injective edge coloring of product graphs and some complexity results
- Creator
- Bhanupriya C.K.; Dominic C.; Sunitha M.S.
- Description
- Three edges e1, e2 and e3 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 e1, e2, e3 are consecutive, then e1 and e3 receive distinct colors. The minimum k for which G has a k-injective edge coloring is called the injective edge chromatic index, denoted by ?? (G) [4]. In this article, the i 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 ?? (G+H) andi?? (G? H) are obtained. Moreover the injective edge i 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. 2023, University of Nis. All rights reserved.
- Source
- Filomat, Vol-37, No. 12, pp. 3963-3983.
- Date
- 2023-01-01
- Publisher
- University of Nis
- Subject
- Cartesian product; complexity; corona; injective edge chromatic index; join; triregular graphs; union
- Coverage
- Bhanupriya C.K., Department of Mathematics, NIT Calicut, Kerala, Kozhikode, 673 601, India, Department of Mathematics, Mar Thoma College Chungathara, Kerala, Malappuram, 679334, India; Dominic C., Department of Mathematics, CHRIST(Deemed to be University), Karnataka, Bengaluru, 560029, India, Department of Mathematical Sciences, University of Essex, Essex, Colchester, CO4 3SQ, United Kingdom; Sunitha M.S., Department of Mathematics, NIT Calicut, Kerala, Kozhikode, 673 601, India
- Rights
- All Open Access; Gold Open Access
- Relation
- ISSN: 3545180
- Format
- Online
- Language
- English
- Type
- Article
Collection
Citation
Bhanupriya C.K.; Dominic C.; Sunitha M.S., “Injective edge coloring of product graphs and some complexity results,” CHRIST (Deemed To Be University) Institutional Repository, accessed February 24, 2025, https://archives.christuniversity.in/items/show/14637.