Results 1 to 10 of about 41,334 (304)

Neighbor full sum distinguishing total coloring of Halin graphs

AIMS Mathematics, 2022
Let $ f: V(G)\cup E(G)\rightarrow \{1, 2, \dots, k\} $ be a total $ k $ -coloring of $ G $. Define a weight function on total coloring as $ \phi(x) = f(x)+\sum\limits_{e\ni x}f(e)+\sum\limits_{y\in N(x)}f(y), $ where $ N(x) = \{y\in V(G)|xy\in E(G)\
Yinwan Cheng, Chao Yang, Bing Yao, Yaqin Luo   +3 more
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General Vertex-Distinguishing Total Coloring of Graphs

Journal of Applied Mathematics, 2014
The general vertex-distinguishing total chromatic number of a graph G is the minimum integer k, for which the vertices and edges of G are colored using k colors such that any two vertices have distinct sets of colors of them and their incident edges.
Chanjuan Liu, Enqiang Zhu
doaj   +1 more source

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, Fekadu Tesgera Agama   +1 more
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Total Rainbow Connection Number of Some Graph Operations

Axioms, 2022
In a graph H with a total coloring, a path Q is a total rainbow if all elements in V(Q)∪E(Q), except for its end vertices, are assigned different colors. The total coloring of a graph H is a total rainbow connected coloring if, for any x,y∈V(H), there is
Hengzhe Li, Yingbin Ma, Yan Zhao
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Exploring Relationship Between Traditional Lattices and Graph Lattices of Topological Coding

Jisuanji kexue yu tansuo, 2021
It is known that there are no polynomial quantum algorithms to solve some lattice difficult problems. Uncolored graphic lattice and colored graphic lattice are the products of multidisciplinary intersection inspired by lattice theory. A uncolored graphic
ZHANG Mingjun, YANG Sihua, YAO Bing
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New Results on Edge-Coloring and Total-Coloring of Split Graphs

Discrete Applied Mathematics, 2023
20 pages, 5 ...
Couto, Fernanda, Ferraz, Diego Amaro, Klein, Sulamita   +2 more
openaire   +3 more sources

Odd-Graceful Total Colorings for Constructing Graphic Lattice

Mathematics, 2021
The security of passwords generated by the graphic lattices is based on the difficulty of the graph isomorphism, graceful tree conjecture, and total coloring conjecture.
Jing Su, Hui Sun, Bing Yao
doaj   +1 more source

Graphs with Bounded Maximum Average Degree and Their Neighbor Sum Distinguishing Total-Choice Numbers

International Journal of Mathematics and Mathematical Sciences, 2017
Let G be a graph and ϕ:V(G)∪E(G)→{1,2,3,…,k} be a k-total coloring. Let w(v) denote the sum of color on a vertex v and colors assigned to edges incident to v.
Patcharapan Jumnongnit, Kittikorn Nakprasit   +1 more
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Planar graphs with $\Delta \geq 7$ and no triangle adjacent to a $C_4$ are minimally edge and total choosable [PDF]

Discrete Mathematics & Theoretical Computer Science, 2016
For planar graphs, we consider the problems of list edge coloring and list total coloring. Edge coloring is the problem of coloring the edges while ensuring that two edges that are adjacent receive different colors.
Marthe Bonamy, Benjamin Lévêque, Alexandre Pinlou   +2 more
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Fractional (P,Q)-Total List Colorings of Graphs

Discussiones Mathematicae Graph Theory, 2013
Let r, s ∈ N, r ≥ s, and P and Q be two additive and hereditary graph properties. A (P,Q)-total (r, s)-coloring of a graph G = (V,E) is a coloring of the vertices and edges of G by s-element subsets of Zr such that for each color i, 0 ≤ i ≤ r − 1, the ...
Kemnitz Arnfried, Mihók Peter, Voigt Margit   +2 more
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