Total coloring conjecture on certain classes of product graphs
| Main Authors: | Somasundaram, Kanagasabapathi; Department of Mathematics Amrita School of Engineering Amrita Vishwa Vidyapeetham University Coimbatore, India, Geetha, Jayabalan; Department of Mathematics Amrita School of Engineering Amrita Vishwa Vidyapeetham University Coimbatore, India, Vignesh, Radhakrishnan; School of Computer Science and Engineering Presidency University Bengaluru India |
|---|---|
| Other Authors: | This research work is supported by SERB-DST (Grant SR/S4/MS: 867/14). |
| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2023
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| Subjects: | |
| Online Access: |
https://www.ejgta.org/index.php/ejgta/article/view/771 https://www.ejgta.org/index.php/ejgta/article/view/771/pdf_265 https://www.ejgta.org/index.php/ejgta/article/downloadSuppFile/771/114 |
Daftar Isi:
- A total coloring of a graph G is an assignment of colors to the elements of the graph G such that no adjacent vertices and edges receive the same color. The total chromatic number of a graph G, denoted by χ′′(G), is the minimum number of colors that suffice in a total coloring. Behzad and Vizing conjectured that for any graph G, Δ(G)+1 ≤ χ′′(G)≤Δ(G)+2, where Δ(G) is the maximum degree of G. In this paper, we prove the Behzad and Vizing conjecture for Indu - Bala product graph, Skew and Converse Skew product graph, Cover product graph, Clique cover product graph and Comb product graph.