Results 11 to 20 of about 6,626,501 (294)
Total Coloring of Claw-Free Planar Graphs [PDF]
Discussiones Mathematicae Graph Theory, 2022 A total coloring of a graph is an assignment of colors to both its vertices and edges so that adjacent or incident elements acquire distinct colors. Let Δ(G) be the maximum degree of G.
Liang Zuosong
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Total Global Dominator Coloring of Trees and Unicyclic Graphs [PDF]
مجلة بغداد للعلوم, 2023 A total global dominator coloring of a graph is a proper vertex coloring of with respect to which every vertex in dominates a color class, not containing and does not dominate another color class.
Chithra K. P., Joseph Mayamma
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Total Coloring of Dumbbell Maximal Planar Graphs
Mathematics, 2022 The Total Coloring Conjecture (TCC) states that every simple graph G is totally (Δ+2)-colorable, where Δ denotes the maximum degree of G. In this paper, we prove that TCC holds for dumbbell maximal planar graphs.
Yangyang Zhou +3 more
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Complexity of Total Dominator Coloring in Graphs
Graphs and Combinatorics, 2023 Let $G=(V,E)$ be a graph with no isolated vertices. A vertex $v$ totally dominate a vertex $w$ ($w \ne v$), if $v$ is adjacent to $w$. A set $D \subseteq V$ called a total dominating set of $G$ if every vertex $v\in V$ is totally dominated by some vertex in $D$. The minimum cardinality of a total dominating set is the total domination number of $G$ and
Michael A. Henning +3 more
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Total Coloring Conjecture for Certain Classes of Graphs
Algorithms, 2018 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.
R. Vignesh, J. Geetha, K. Somasundaram
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A decomposition for total‐coloring partial‐grids and list‐total‐coloring outerplanar graphs
Networks, 2011 AbstractThe total chromatic number χT(G) is the least number of colors sufficient to color the elements (vertices and edges) of a graph G in such a way that no incident or adjacent elements receive the same color. In the present work, we obtain two results on total‐coloring. First, we extend the set of partial‐grids classified with respect to the total‐
Raphael C. S. Machado +1 more
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2-Quasitotal Fuzzy Graphs and Their Total Coloring
Advances in Fuzzy Systems, 2020 Coloring of fuzzy graphs has many real-life applications in combinatorial optimization problems like traffic light system, exam scheduling, and register allocation. The coloring of total fuzzy graphs and its applications are well studied. This manuscript
V. N. Srinivasa Rao Repalle +1 more
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Equitable total coloring of Cm□Cn [PDF]
Discrete Applied Mathematics, 2009 AbstractThe equitable total chromatic number of a graph G is the smallest integer k for which G has a k-total coloring such that the number of vertices and edges colored with each color differs by at most one. In this paper, we show that the Cartesian product graphs of Cm and Cn have equitable total 5-coloring for all m≥3 and n≥3.
Chunling Tong +3 more
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Oriented total-coloring of oriented graphs
Discrete MathematicszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bensmail, Julien +6 more
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Edge and total coloring of interval graphs [PDF]
Discrete Applied Mathematics, 2001 Let \(\chi_e(G)\) and \(\chi_{ve}(G)\) be the edge and total chromatic number of a graph \(G\). It is clear that \(\chi_{e}(G)\geq\Delta(G)\) and \(\chi_{ve}(G)\geq\Delta(G)+1\), where \(\Delta(G)\) is the maximum degree of \(G\). By Vizing's theorem, \(\chi_{e}(G)\leq\Delta(G)+1\) for each \(G\).
Bojarshinov, V.A.
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