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On adjacent vertex distinguishing total coloring of quadrilateral snake [PDF]

JOURNAL OF ADVANCES IN MATHEMATICS, 2017
In this paper, we prove the existence of the adjacent vertex distinguishing total coloringnof quadrilateral snake, double quadrilateral snake, alternate quadrilateral snake and double alternate quadrilateral snake in detail. Also, we present an algorithm to obtain the adjacent vertex distinguishing total coloring of these quadrilateral graph family ...
K Thirusangu, R Ezhilarasi
semanticscholar   +5 more sources

Adjacent vertex distinguishing total coloring of corona products (Brief Announcement)

Procedia Computer Science, 2023
An adjacent vertex distinguishing total k-coloring f of a graph G is a proper total k-coloring of G such that no pair of adjacent vertices has the same color sets. In 2005 Zhang et al. posted the conjecture (AVDTCC) that every simple graph G has adjacent vertex distinguishing total (∆(G) + 3)-coloring.
Hanna Furmańczyk, Rita Zuazua
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Adjacent Vertex Distinguishing Coloring of Fuzzy Graphs

Mathematics, 2023
In this paper, we consider the adjacent vertex distinguishing proper edge coloring (for short, AVDPEC) and the adjacent vertex distinguishing total coloring (for short, AVDTC) of a fuzzy graph.
Zengtai Gong, Chen Zhang
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Adjacent vertex distinguishing total coloring of the corona product of graphs

Discussiones Mathematicae Graph Theory
Summary: An adjacent vertex distinguishing (AVD-)total coloring of a simple graph \(G\) is a proper total coloring of \(G\) such that for any pair of adjacent vertices \(u\) and \(v\), we have \(C(u)\neq C(v)\), where \(C(u)\) is the set of colors given to vertex \(u\) and the edges incident to \(u\) for \(u\in V(G)\). The AVD-total chromatic number, \(
Shaily Verma, B. S. Panda
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Adjacent vertex strongly distinguishing total coloring of graphs with lower average degree

Discussiones Mathematicae Graph Theory
Summary: An adjacent vertex strongly distinguishing total-coloring of a graph \(G\) is a proper total-coloring such that no two adjacent vertices meet the same color set, where the color set of a vertex consists of all colors assigned on the vertex and its incident edges and neighbors. The minimum number of the colors required is called adjacent vertex
Fei Wen, Li Zhou, Zepeng Li
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Adjacent vertex distinguishing total coloring of graphs with maximum degree 4

Discrete Mathematics, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lu, You, Li, Jiaao, Luo, Rong, Miao, Zhengke   +3 more
semanticscholar   +4 more sources

Adjacent vertex distinguishing total coloring of planar graphs with maximum degree 9

Discrete Mathematics, 2019
For a simple graph $G$, an adjacent vertex distinguishing (or AVD) total $k$-coloring is a proper total $k$-coloring of $G$ such that any two adjacent vertices have different color sets; a color set for vertex $v$ consisting of the color of $v$ and the colors of its incidence edges.
Jie Hu, Guanghui Wang, Jianliang Wu, Donglei Yang, Xiaowei Yu   +4 more
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Adjacent vertex distinguishing total coloring of corona product of graphs [PDF]

Ars Mathematica Contemporanea, 2022
An adjacent vertex distinguishing total $k$-coloring $f$ of a graph $G$ is a proper total $k$-coloring of $G$ such that no pair of adjacent vertices has the same color sets, where the color set at a vertex $v$, $C^G_f(v)$, is $\{f(v)\} \cup \{f(vu)|u \in V (G), vu \in E(G)\}$. In 2005 Zhang et al. posted the conjecture (AVDTCC) that every simple graph $
Furmańczyk, Hanna, Zuazua, Rita
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Adjacent vertex distinguishing edge-colorings and total-colorings of the Cartesian product of graphs

Numerical Algebra, Control & Optimization, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tian, Shuangliang, Chen, Ping, Shao, Yabin, Wang, Qian   +3 more
semanticscholar   +6 more sources

Incidence-Adjacent Vertex Distinguishing Equitable Total Coloring of Mycielski Graphs

2020 4th International Conference on Computer Engineering, Information Science & Application Technology (ICCIA 2020), 2020
: The incidence-adjacent vertex distinguishing equitable total coloring of the Myceilski graphs of path, cycle, wheel and fan are discussed, and of which the incidence-adjacent vertex distinguishing equitable total chromatic numbers are confirmed ...
Jishun Wang, Lin Zuo, Renfu Ge, Bujun Li
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