Results 1 to 10 of about 1,402,502 (197)
On the total chromatic edge stability number and the total chromatic subdivision number of graphs [PDF]
Discrete Mathematics Letters, 2022 Summary: A proper total coloring of a graph \(G\) is an assignment of colors to the vertices and edges of \(G\) (together called the elements of \(G\)) such that neighbored elements -- two adjacent vertices or two adjacent edges or a vertex and an incident edge -- are colored differently.
Arnfried Kemnitz, Massimiliano Marangio
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Snarks with total chromatic number 5 [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 Graph ...
Gunnar Brinkmann +2 more
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The Local Antimagic Total Chromatic Number of Some Wheel-Related Graphs
Axioms, 2022 Let G=(V,E) be a connected graph with |V|=n and |E|=m. A bijection f:V(G)∪E(G)→{1,2,⋯,n+m} is called local antimagic total labeling if, for any two adjacent vertices u and v, ωt(u)≠ωt(v), where ωt(u)=f(u)+∑e∈E(u)f(e), and E(u) is the set of edges ...
Xue Yang +3 more
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On the coequal values of total chromatic number and chromatic index
Journal of Combinatorial Theory, Series B, 2023 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Guantao Chen, Yanli Hao
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Total dominator chromatic number of Kneser graphs
AKCE International Journal of Graphs and Combinatorics, 2023 Decomposition into special substructures inheriting significant properties is an important method for the investigation of some mathematical structures. A total dominator coloring (briefly, a TDC) of a graph G is a proper coloring (i.e.
Parvin Jalilolghadr, Ali Behtoei
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Local total anti-magic chromatic number of graphs
Heliyon, 2023 Let G=(V,E) be a graph without isolated vertices and let |V(G)|=n and |E(G)|=m. A bijection π:V(G)∪E(G)→{1,2,....,n+m} is said to be local total anti-magic labeling of a graph G if it satisfies the conditions: (i.) for any edge uv, ω(u)≠ω(v), where u and
V. Sandhiya, M. Nalliah
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Total Chromatic Number for Some Classes of Cayley Graphs [PDF]
Soft Computing, 2022 Abstract In this paper, we have obtained the total chromatic number for some classes of Cayley graphs, particularly the Unitary Cayley graphs on even order and some other Circulant graphs. We have also proved the Total coloring conjecture for some perfect Cayley graphs.MSC Classification: 05C15 (Primary), 05B15 (Secondary)
S. Prajnanaswaroopa +2 more
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Neighbor Sum Distinguishing Total Chromatic Number of Planar Graphs without 5-Cycles
Discussiones Mathematicae Graph Theory, 2020 For a given graph G = (V (G), E(G)), a proper total coloring ϕ: V (G) ∪ E(G) → {1, 2, . . . , k} is neighbor sum distinguishing if f(u) ≠ f(v) for each edge uv ∈ E(G), where f(v) = Σuv∈E(G) ϕ(uv)+ϕ(v), v ∈ V (G). The smallest integer k in such a coloring
Zhao Xue, Xu Chang-Qing
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On the Total Set Chromatic Number of Graphs
Theory and Applications of Graphs, 2022 Given a vertex coloring c of a graph, the neighborhood color set of a vertex is defined to be the set of all of its neighbors’ colors. The coloring c is called a set coloring if any two adjacent vertices have different neighborhood color sets.
Mark Anthony C. Tolentino +2 more
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Total dominator chromatic number of a graph [PDF]
Transactions on Combinatorics, 2015 Given a graph $G$, the total dominator coloring problem seeks a proper coloring of $G$ with the additional property that every vertex in the graph is adjacent to all vertices of a color class. We seek to minimize the number of color classes.
Adel P. Kazemi
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