Total colouring of some cartesian and direct product graphs

Authors

DOI:

https://doi.org/10.11575/cdm.v15i1.62679

Abstract

A graph is $k$-total colourable if there is an assignment of $k$ different colours to the vertices and edges of the graph such that no two adjacent nor incident elements receive the same colour. The total chromatic number of some direct product graphs are determined. In particular, a sufficient condition is given for direct products of bipartite graphs to have total chromatic number equal to its maximum degree plus one. Partial results towards the total chromatic number of $K_n\times K_m$ are also established.

Author Biographies

Kyle MacKeigan, Dalhousie University

Mathematics and teaching assistant

Jeannette Janssen, Dalhousie University

Mathematics and Professor

References

Behzad M.

Geetha J.

Somasundaram K.

Hammack R.

Kemnitz A.

Marangio M.

Pranavar K.

Seoud M.A.

Tong C.

Vizing V.G.

Zmazek B.

Downloads

Published

2020-05-11

Issue

Section

Articles