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A genetic algorithm for total graph coloring
Journal of Intelligent & Fuzzy Systems, 2019 A genetic algorithm (GA) belongs to the class of evolutionary algorithms and it is one of the most studied heuristic algorithms to solve graph coloring problems. In this paper, we propose a new GA algorithm for the total graph coloring problem. To the best of our knowledge, no algorithm based on a GA exists in the literature for total graph coloring ...
Arindam Dey 0002 +6 more
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Total Colorings of Degenerated Graphs
Combinatorica, 2001A total coloring of a graph G is a coloring of all elements of G, i.e. vertices and edges, such that no two adjacent or incident elements receive the same color. A graph G is s-degenerate for a positive integer s if G can be reduced to a trivial graph by successive removal of vertices with degree ≤s.
Shuji Isobe +2 more
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Total Colorings of Graphs with Minimum Sum of Colors
Graphs and Combinatorics, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ewa M. Kubicka +2 more
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Total Colorings of Product Graphs
Graphs and Combinatorics, 2018A 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.
J. Geetha 0001, K. Somasundaram 0001
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Total colorings of circulant graphs
Discrete Mathematics, Algorithms and Applications, 2020The total chromatic number [Formula: see text] is the least number of colors needed to color the vertices and edges of a graph [Formula: see text] such that no incident or adjacent elements (vertices or edges) receive the same color. Behzad and Vizing proposed a well-known total coloring conjecture (TCC): [Formula: see text], where [Formula: see text]
J. Geetha 0001 +2 more
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Uniquely Total Colorable Graphs
Graphs and Combinatorics, 1997A total coloring of a graph is an assignment of colors to the vertices and edges of the graph so that no two adjacent edges have the same color, no two adjacent vertices have the same color and no vertex and an incident edge have the same color. The minimum number of colors needed by a total coloring is called the total chromatic number and is denoted \
Saieed Akbari +3 more
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Total coloring of the prismatic graphs
Discrete Mathematics, Algorithms and Applications, 2020A total coloring of a graph is an assignment of colors to all the elements of the graph such that no two adjacent or incident elements receive the same color. A graph [Formula: see text] is prismatic, if for every triangle [Formula: see text], every vertex not in [Formula: see text] has exactly one neighbor in [Formula: see text].
S. Mohan, K. Somasundaram 0001
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Total Dominator Colorings and Total Domination in Graphs
Graphs and Combinatorics, 2014Given a graph \(G\), a total dominator coloring is a proper coloring of the vertices of \(G\) in which each vertex is adjacent to every vertex of some color class. The total dominator chromatic number \(\chi_{d}^{t}(G)\) of \(G\) is the minimum number of colors among all total dominator colorings of \(G\). A total dominating set of \(G\) is a set \(S\)
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Totally symmetric colored graphs
Journal of Graph Theory, 2009AbstractIn this paper we describe almost all edge‐colored complete graphs that are fully symmetric with respect to colors and transitive on every set of edges of the same color. This generalizes the recent description of self‐complementary symmetric graphs by Peisert and gives examples of permutation groups that require more than 5 colors to be ...
Mariusz Grech, Andrzej Kisielewicz 0001
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