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2022 ◽  
Vol 48 (10) ◽  
Author(s):  
Luis Gustavo Gonzaga ◽  
Sheila de Almeida ◽  
Cândida da Silva ◽  
Jadder Cruz
Keyword(s):  

2022 ◽  
Vol 48 (11) ◽  
Author(s):  
Isabel Gonçalves ◽  
Simone Dantas ◽  
Diana Sasaki
Keyword(s):  

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 109
Author(s):  
Jing Su ◽  
Hui Sun ◽  
Bing Yao

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. A graphic lattice is generated by a graphic base and graphical operations, where a graphic base is a group of disjointed, connected graphs holding linearly independent properties. We study the existence of graphic bases with odd-graceful total colorings and show graphic lattices by vertex-overlapping and edge-joining operations; we prove that these graphic lattices are closed to the odd-graceful total coloring.


2021 ◽  
Vol 37 (4) ◽  
pp. 738-746
Author(s):  
Yu-lin Chang ◽  
Fei Jing ◽  
Guang-hui Wang ◽  
Ji-chang Wu

Author(s):  
A. Zorzi ◽  
C.M.H. Figueiredo ◽  
R.C.S. Machado ◽  
L.M. Zatesko ◽  
U.S. Souza
Keyword(s):  

2021 ◽  
pp. 2142001
Author(s):  
Yingbin Ma ◽  
Wenhan Zhu

Let [Formula: see text] be an edge-colored graph with order [Formula: see text] and [Formula: see text] be a fixed integer satisfying [Formula: see text]. For a vertex set [Formula: see text] of at least two vertices, a tree containing the vertices of [Formula: see text] in [Formula: see text] is called an [Formula: see text]-tree. The [Formula: see text]-tree [Formula: see text] is a total-rainbow [Formula: see text]-tree if the elements of [Formula: see text], except for the vertex set [Formula: see text], have distinct colors. A total-colored graph [Formula: see text] is said to be total-rainbow [Formula: see text]-tree connected if for every set [Formula: see text] of [Formula: see text] vertices in [Formula: see text], there exists a total-rainbow [Formula: see text]-tree in [Formula: see text], while the total-coloring of [Formula: see text] is called a [Formula: see text]-total-rainbow coloring. The [Formula: see text]-total-rainbow index of a nontrivial connected graph [Formula: see text], denoted by [Formula: see text], is the smallest number of colors needed in a [Formula: see text]-total-rainbow coloring of [Formula: see text]. In this paper, we show a sharp upper bound for [Formula: see text], where [Formula: see text] is a 2-connected or 2-edge-connected graph.


2021 ◽  
Vol 27 (1) ◽  
pp. 31-38
Author(s):  
D. Muthuramakrishnan ◽  
G. Jayaraman
Keyword(s):  

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 708
Author(s):  
Donghan Zhang

A theta graph Θ2,1,2 is a graph obtained by joining two vertices by three internally disjoint paths of lengths 2, 1, and 2. A neighbor sum distinguishing (NSD) total coloring ϕ of G is a proper total coloring of G such that ∑z∈EG(u)∪{u}ϕ(z)≠∑z∈EG(v)∪{v}ϕ(z) for each edge uv∈E(G), where EG(u) denotes the set of edges incident with a vertex u. In 2015, Pilśniak and Woźniak introduced this coloring and conjectured that every graph with maximum degree Δ admits an NSD total (Δ+3)-coloring. In this paper, we show that the listing version of this conjecture holds for any IC-planar graph with maximum degree Δ≥9 but without theta graphs Θ2,1,2 by applying the Combinatorial Nullstellensatz, which improves the result of Song et al.


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