We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Total Coloring Conjecture for Certain Classes of Graphs.
- Authors
Vignesh, R.; Geetha, J.; Somasundaram, K.
- Abstract
A total coloring of a graph G is an assignment of colors to the elements of the graph G such that no two adjacent or incident elements 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 total coloring conjecture for certain classes of graphs of deleted lexicographic product, line graph and double graph.
- Subjects
GRAPH coloring; MATHEMATICS theorems; BIPARTITE graphs; GEOMETRIC vertices; COMPLETE graphs
- Publication
Algorithms, 2018, Vol 11, Issue 10, p161
- ISSN
1999-4893
- Publication type
Article
- DOI
10.3390/a11100161