Results 11 to 20 of about 41,334 (304)
AKCE International Journal of Graphs and Combinatorics, 2023 The smallest integer k needed for the assignment of k colors to the elements so that the coloring is proper (vertices and edges) is called the total chromatic number of a graph.
Jayabalan Geetha +2 more
doaj +4 more sources
Equitable Total Coloring of Corona of Cubic Graphs
Discussiones Mathematicae Graph Theory, 2021 The minimum number of total independent partition sets of V ∪ E of a graph G = (V, E) is called the total chromatic number of G, denoted by X′(G). If the di erence between cardinalities of any two total independent sets is at most one, then the minimum ...
Furmańczyk Hanna, Zuazua Rita
doaj +3 more sources
Total fuzzy graph coloring [PDF]
Journal of Hyperstructures, 2023 In this paper, a hybrid genetic algorithm (HGA) is proposed for the total fuzzy graph coloring (TFGC) problem. TFGC comprises of a graph with fuzzy vertices and edges, seeks to obtain an optimal $k-$coloring of that fuzzy graph such that the degree of ...
Smriti Saxena +2 more
doaj +2 more sources
Vertex-Distinguishing IE-Total Colorings of Complete Bipartite Graphs Km,N(m < n) [PDF]
Discussiones Mathematicae Graph Theory, 2013 Let G be a simple graph. An IE-total coloring f of G is a coloring of the vertices and edges of G so that no two adjacent vertices receive the same color. Let C(u) be the set of colors of vertex u and edges incident to u under f. For an IE-total coloring
Chen Xiang’en, Gao Yuping, Yao Bing
doaj +2 more sources
Total Coloring of Claw-Free Planar Graphs
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
doaj +2 more sources
Generalized Fractional Total Colorings of Graphs
Discussiones Mathematicae Graph Theory, 2015 Let P and Q be additive and hereditary graph properties and let r, s be integers such that r ≥ s. Then an r/s -fractional (P,Q)-total coloring of a finite graph G = (V,E) is a mapping f, which assigns an s-element subset of the set {1, 2, . . .
Karafová Gabriela, Soták Roman
doaj +3 more sources
Total Dominator Colorings In Cycles
, 2012 Determining the total dominator chromatic number in cycles.
A. Vijayalekshmi
+6 more sources
Total coloring graphs with large maximum degree [PDF]
Journal of Graph TheoryABSTRACTWe prove that for any graph , the total chromatic number of is at most . This saves one color in comparison with the result of Hind from 1992. In particular, our result says that if , then has a total coloring using at most colors. When is regular and has a sufficient number of vertices, we can actually save an additional two colors ...
Aseem Dalal +2 more
openalex +4 more sources
From semi-total to equitable total colorings [PDF]
Independently posed by Behzad and Vizing, the Total Coloring Conjecture asserts that the total chromatic number of a simple connected graph $G$ is either $Δ(G)+1$ or $Δ(G)+2$, where $Δ(G)$ is the largest degree of any vertex of $G$. To decide whether a cubic graph $G$ has total chromatic number $Δ(G)+1$, even for bipartite cubic graphs, is NP-hard ...
I. J. Dejter
openalex +3 more sources
Generalized Fractional and Circular Total Colorings of Graphs
Discussiones Mathematicae Graph Theory, 2015 Let P and Q be additive and hereditary graph properties, r, s ∈ N, r ≥ s, and [ℤr]s be the set of all s-element subsets of ℤr. An (r, s)-fractional (P,Q)-total coloring of G is an assignment h : V (G) ∪ E(G) → [ℤr]s such that for each i ∈ ℤr the ...
Kemnitz Arnfried +4 more
doaj +2 more sources