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Connectivity of Direct Products of Graphs
Ars Comb., 2011 Let $κ(G)$ be the connectivity of $G$ and $G\times H$ the direct product of $G$ and $H$. We prove that for any graphs $G$ and $K_n$ with $n\ge 3$, $κ(G\times K_n)=min\{nκ(G),(n-1)δ(G)\}$, which was conjectured by Guji and Vumar.
Wei Wang 0052, Ni-Ni Xue
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Computing the (k-)monopoly Number of Direct Product of Graphs [PDF]
, 2015 . Let G = (V,E) be a simple graph without isolated vertices and minimum degree δ(G), and let k ∈ {1 − dδ(G)/2e,..., bδ(G)/2c} be an integer. Given a set M ⊂ V, a vertex v of G is said to be k-controlled by M if δM(v) ≥ δ(v)2 + k where δM(v) represents ...
Iztok Peterinb +5 more
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Proper Connection Of Direct Products
Discussiones Mathematicae Graph Theory, 2017 The proper connection number of a graph is the least integer k for which the graph has an edge coloring with k colors, with the property that any two vertices are joined by a properly colored path.
Hammack Richard H., Taylor Dewey T.
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Intuitionistic Fuzzy Graphs with Categorical Properties
Fuzzy Information and Engineering, 2015 The main purpose of this paper is to show the rationality of some operations, defined or to be defined, on intuitionistic fuzzy graphs. Firstly, three kinds of new product operations (called direct product, lexicographic product, and strong product) are ...
Hossein Rashmanlou +3 more
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Construction of Mutually Orthogonal Graph Squares Using Novel Product Techniques
Journal of Mathematics, 2022 Sets of mutually orthogonal Latin squares prescribe the order in which to apply different treatments in designing an experiment to permit effective statistical analysis of results, they encode the incidence structure of finite geometries, they ...
A. El-Mesady, Omar Bazighifan
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Outer Independent Double Italian Domination of Some Graph Products
Theory and Applications of Graphs, 2023 An outer independent double Italian dominating function on a graph $G$ is a function $f:V(G)\rightarrow\{0,1,2,3\}$ for which each vertex $x\in V(G)$ with $\color{red}{f(x)\in \{0,1\}}$ then $\sum_{y\in N[x]}f(y)\geqslant 3$ and vertices assigned $0 ...
Rouhollah Jalaei, Doost Ali Mojdeh
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Certain Operations on Complex Picture Fuzzy Graphs
IEEE Access, 2022 A complex picture fuzzy set (Com-PFS) is a motivating tool for more precisely interpreting fuzzy notions. Recently, all extensions of complex fuzzy graphs (Com-FGs) have become a growing research topic as they handle ambiguous situations more explicitly ...
Muhammad Shoaib +4 more
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Cartesian products of directed graphs with loops [PDF]
Discrete Mathematics, 2018 12 pages, 1 ...
Wilfried Imrich, Iztok Peterin
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On the super connectivity of direct product of graphs
RAIRO - Operations Research, 2022 A vertex-cut S is called a super vertex-cut if G − S is disconnected and it contains no isolated vertices. The super-connectivity, κ′, is the minimum cardinality over all super vertex-cuts. This article provides bounds for the super connectivity of the direct product of an arbitrary graph and the complete graph Kn.
Farnaz Soliemany +2 more
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Complex Vague Graphs and Their Application in Decision-Making Problems
IEEE Access, 2020 Fuzzy graph models are found everywhere in natural and human made structures, including process dynamics in biological, physical and social systems. Since real-life problems are often uncertain due to inconsistent and indeterminate information, it is ...
Shouzhen Zeng +4 more
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