Results 21 to 30 of about 59,909 (247)
On Cartesian Products of Signed Graphs [PDF]
Discrete Applied Mathematics, 2020 In this paper, we study the Cartesian product of signed graphs as defined by Germina, Hameed and Zaslavsky (2011). Here we focus on its algebraic properties and look at the chromatic number of some Cartesian products. One of our main results is the unicity of the prime factor decomposition of signed graphs.
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Game Chromatic Number of Cartesian Product Graphs [PDF]
The Electronic Journal of Combinatorics, 2008 The game chromatic number $\chi _{g}$ is considered for the Cartesian product $G\,\square \,H$ of two graphs $G$ and $H$. Exact values of $\chi _{g}(K_2\square H)$ are determined when $H$ is a path, a cycle, or a complete graph. By using a newly introduced "game of combinations" we show that the game chromatic number is not bounded in the class of ...
Bartnicki, T. +5 more
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Distinguishing Cartesian products of countable graphs
Discussiones Mathematicae Graph Theory, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Estaji Ehsan +4 more
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Strong Products of Hypergraphs: Unique Prime Factorization Theorems and Algorithms [PDF]
, 2013 It is well-known that all finite connected graphs have a unique prime factor decomposition (PFD) with respect to the strong graph product which can be computed in polynomial time.
Hellmuth, Marc +2 more
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Distance magic Cartesian product of graphs
Discussiones Mathematicae Graph Theory, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cichacz Sylwia +3 more
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Dispersion on Certain Cartesian Products of Graphs
, 2023 In this short note we prove a sharp dispersive estimate $\|\mathrm{e}^{\mathrm{i} tH} f\|_\infty < t^{-d/3}\|f\|_1$ for any Cartesian product $\mathbb{Z}^d\mathop\square G_F$ of the integer lattice and a finite graph. This includes the infinite ladder, $k$-strips and infinite cylinders, which can be endowed with certain potentials.
Ammari, Kaïs, Sabri, Mostafa
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On Path-Pairability in the Cartesian Product of Graphs
Discussiones Mathematicae Graph Theory, 2016 We study the inheritance of path-pairability in the Cartesian product of graphs and prove additive and multiplicative inheritance patterns of path-pairability, depending on the number of vertices in the Cartesian product.
Mészáros Gábor
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On primality of Cartesian product of graphs [PDF]
Arab Journal of Mathematical SciencesPurposeThe present work focuses on the primality and the Cartesian product of graphs.Design/methodology/approachGiven a graph G, a subset M of V (G) is a module of G if, for a, b ∈ M and x ∈ V (G) \ M, xa ∈ E(G) if and only if xb ∈ E(G).
Nadia El Amri +2 more
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Retract rigid cartesian products of graphs
Discrete Mathematics, 1988 A graph H is defined to be a retract of the graph G if there are edge- preserving maps \(f: V(H)\to V(G)\) and \(g: V(G)\to V(H)\) such that \(g(f(v))=v,\) for each \(v\in V(G)\) \((''v\in V(G)''\) appears in the paper, but \(''v\in V(H)''\) is correct). Thus H can be regarded as a subgraph of G.
Nowakowski, Richard, Rival, Ivan
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GRACEFUL CHROMATIC NUMBER OF SOME CARTESIAN PRODUCT GRAPHS
Ural Mathematical Journal, 2023 A graph \(G(V,E)\) is a system consisting of a finite non empty set of vertices \(V(G)\) and a set of edges \(E(G)\). A (proper) vertex colouring of \(G\) is a function \(f:V(G)\rightarrow \{1,2,\ldots,k\},\) for some positive integer \(k\) such that ...
I Nengah Suparta +3 more
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