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Super Connected Direct Product of Graphs and Cycles
Axioms, 2022 The topology of an interconnection network can be modeled by a graph G=(V(G),E(G)). The connectivity of graph G is a parameter used to measure the reliability of a corresponding network. The direct product is an important graph product. This paper mainly
Jiaqiong Yin, Yingzhi Tian
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Hyperbolicity of Direct Products of Graphs [PDF]
Symmetry, 2018 It is well-known that the different products of graphs are some of the more symmetric classes of graphs. Since we are interested in hyperbolicity, it is interesting to study this property in products of graphs. Some previous works characterize the hyperbolicity of several types of product graphs (Cartesian, strong, join, corona and lexicographic ...
Walter Carballosa +2 more
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On 3-Colorings of Direct Products of Graphs
Discussiones Mathematicae Graph Theory, 2019 The k-independence number of a graph G, denoted as αk(G), is the order of a largest induced k-colorable subgraph of G. In [S. Špacapan, The k-independence number of direct products of graphs, European J. Combin.
Špacapan Simon
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Dominating the Direct Product of Two Graphs through Total Roman Strategies
Mathematics, 2020 Given a graph G without isolated vertices, a total Roman dominating function for G is a function f:V(G)→{0,1,2} such that every vertex u with f(u)=0 is adjacent to a vertex v with f(v)=2, and the set of vertices with positive labels induces a graph of ...
Abel Cabrera Martínez +3 more
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On direct product cancellation of graphs
Discrete Mathematics, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Richard H Hammack
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Distance regularity in direct-product graphs
Applied Mathematics Letters, 2000 Let \(G=(V,E)\) and \(H=(W,F)\) be graphs. The direct product \(G\times H\) of \(G\) and \(H\) is defined as follows: \(V(G\times H)=V\times W\) and \(E(G\times H)=\{\{(u,x),(v,y)\}:\{u,v\}\in E, \{x,y\}\in F\}\). In this paper the following results are obtained. If \(G\) and \(H\) are distance regular graphs of diameter at least two, then \(G\times H\)
Aggarwal, S., Jha, P. K., Vikram, M.
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A quasicancellation property for the direct product of graphs
Discrete Mathematics, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Richard H Hammack
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The b-chromatic index of direct product of graphs
Discrete Applied Mathematics, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ivo Koch, Iztok Peterin
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Unexpected automorphisms in direct product graphs
Journal of Combinatorial Theory Series BzbMATH Open Web Interface contents unavailable due to conflicting licenses.
Binzhou Xia
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Resolvability and Strong Resolvability in the Direct Product of Graphs [PDF]
Results in Mathematics, 2016 Given a connected graph $G$, a vertex $w\in V(G)$ distinguishes two different vertices $u,v$ of $G$ if the distances between $w$ and $u$ and between $w$ and $v$ are different. Moreover, $w$ strongly resolves the pair $u,v$ if there exists some shortest $u-w$ path containing $v$ or some shortest $v-w$ path containing $u$.
Dorota Kuziak +2 more
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