Results 31 to 40 of about 502 (87)

Total Colourings of Direct Product Graphs

, 2019
A graph is k-total colourable if there is an assignment of k different colours to the vertices and edges of the graph such that no two adjacent nor incident elements receive the same colour.
Janssen, Jeannette, MacKeigan, Kyle
core   +1 more source

Domination Parameters of the Unitary Cayley Graph of 𝕑/n𝕑

Discussiones Mathematicae Graph Theory, 2023
The unitary Cayley graph of 𝕑/n𝕑, denoted Xn, is the graph with vertex set {0, . . ., n − 1} where vertices a and b are adjacent if and only if gcd(a − b, n) = 1.
Burcroff Amanda
doaj   +1 more source

The competition number of a generalized line graph is at most two

, 2012
In 1982, Opsut showed that the competition number of a line graph is at most two and gave a necessary and sufficient condition for the competition number of a line graph being one.
Park, Boram, Sano, Yoshio
core   +3 more sources

Soft covering based rough graphs and corresponding decision making

Open Mathematics, 2019
Soft set theory and rough set theory are two new tools to discuss uncertainty. Graph theory is a nice way to depict certain information. Particularly soft graphs serve the purpose beautifully.
Park Choonkil, Shah Nasir, Rehman Noor, Ali Abbas, Ali Muhammad Irfan, Shabir Muhammad   +5 more
doaj   +1 more source

Generalized 4-connectivity of hierarchical star networks

Open Mathematics, 2022
The connectivity is an important measurement for the fault-tolerance of a network. The generalized connectivity is a natural generalization of the classical connectivity. An SS-tree of a connected graph GG is a tree T=(V′,E′)T=\left(V^{\prime} ,E^{\prime}
Wang Junzhen, Zou Jinyu, Zhang Shumin
doaj   +1 more source

Integral Laplacian graphs with a unique repeated Laplacian eigenvalue, I

Special Matrices, 2023
The set Si,n={0,1,2,…,n−1,n}\{i}{S}_{i,n}=\left\{0,1,2,\ldots ,n-1,n\right\}\setminus \left\{i\right\}, 1⩽i⩽n1\leqslant i\leqslant n, is called Laplacian realizable if there exists an undirected simple graph whose Laplacian spectrum is Si,n{S}_{i,n}. The
Hameed Abdul, Tyaglov Mikhail
doaj   +1 more source

The Cordial Labeling for the Four-Leaved Rose Graph

, 2018
A cactus graph with four blocks which are all cycles, not necessarily be of the same size, is called four-leaved rose graph and denoted by Ln, m, k, s, where n, m, k and s represent she sizes of the four cycles.
A. Elrokh
semanticscholar   +1 more source

A note on the partition dimension of Cartesian product graphs

, 2010
Let $G=(V,E)$ be a connected graph. The distance between two vertices $u,v\in V$, denoted by $d(u, v)$, is the length of a shortest $u-v$ path in $G$. The distance between a vertex $v\in V$ and a subset $P\subset V$ is defined as $min\{d(v, x): x \in P\}$
Rodriquez-Velazquez, Juan A., Yero, Ismael G.   +1 more
core   +1 more source

Weak Total Resolvability In Graphs

Discussiones Mathematicae Graph Theory, 2016
A vertex v ∈ V (G) is said to distinguish two vertices x, y ∈ V (G) of a graph G if the distance from v to x is di erent from the distance from v to y.
Casel Katrin, Estrada-Moreno Alejandro, Fernau Henning, Rodríguez-Velázquez Juan Alberto   +3 more
doaj   +1 more source

On Grundy Total Domination Number in Product Graphs

Discussiones Mathematicae Graph Theory, 2021
A longest sequence (v1, . . ., vk) of vertices of a graph G is a Grundy total dominating sequence of G if for all i, N(υj)\∪j=1i-1N(υj)≠∅N({\upsilon _j})\backslash \bigcup\nolimits_{j = 1}^{i - 1} {N({\upsilon _j})} \ne \emptyset .
Brešar Boštjan, Bujtás Csilla, Gologranc Tanja, Klavžar Sandi, Košmrlj Gašper, Marc Tilen, Patkós Balázs, Tuza Zsolt, vizer Máté   +8 more
doaj   +1 more source