Total colorings of product graphs
type: Item
instance of: scholarly article
title: Total colorings of product graphs
zbMATH Open document ID: 1388.05065
author: J. Geetha
author: K. Somasundaram
published in: Graphs and Combinatorics
publication date: 2018-04-13T00:00:00Z
review text: A proper total coloring of a graph \(G\) is an assignment of colors to vertices and edges of the graph, such that adjacent and incident elements receive different colors. The total chromatic number \(\chi^{\prime\prime}(G)\) of the graph \(G\) is the minimum number of colors needed for a proper total coloring. Clearly, if \(\Delta\) is the maximum degree of \(G\), then \(\Delta+1 \leq \chi^{\prime\prime}(G)\). The Behzad-Vizing total coloring conjecture asserts that for all graphs \(\chi^{\prime\prime}(G)=\Delta+1\) or \( \chi^{\prime\prime}(G)=\Delta+2\). The paper verifies the conjecture for various products of certain classes of graphs.
reviewed by: László A. Székely
Mathematics Subject Classification ID: 05C15
Mathematics Subject Classification ID: 05C76
zbMATH DE Number: 6859819
zbMATH Keywords: product graphs
zbMATH Keywords: direct product
zbMATH Keywords: strong product
zbMATH Keywords: lexicographic product
zbMATH Keywords: total coloring
MaRDI profile type: Publication
full work available at URL: s00373-018-1876-x
OpenAlex ID: W2792907414
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DOI: 10.1007/S00373-018-1876-X
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description: scientific article; zbMATH DE number 6859819