Results 31 to 40 of about 59,758 (255)
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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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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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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Isoperimetric Inequalities for Cartesian Products of Graphs [PDF]
Combinatorics, Probability and Computing, 1998 The authors define another number (isoperimetric invariant) describing the bisection behavior of graphs with weights on vertices and edges, which specializes to Mohar's isoperimetric number and to the Cheeger constant for some choices of weights. They prove an alternative characterization of this number which replaces the minimum over the bisections of
Chung, F. R. K., Tetali, Prasad
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Prime Factorization And Domination In The Hierarchical Product Of Graphs
Discussiones Mathematicae Graph Theory, 2017 In 2009, Barrière, Dalfó, Fiol, and Mitjana introduced the generalized hierarchical product of graphs. This operation is a generalization of the Cartesian product of graphs.
Anderson S.E. +3 more
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Spectral properties of the hierarchical product of graphs [PDF]
, 2016 The hierarchical product of two graphs represents a natural way to build a larger graph out of two smaller graphs with less regular and therefore more heterogeneous structure than the Cartesian product.
Skardal, Per Sebastian, Wash, Kirsti
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The adjacency spectrum of two new operations of graphs
AKCE International Journal of Graphs and Combinatorics, 2018 Let be a graph and be its adjacency matrix. The eigenvalues of are the eigenvalues of and form the adjacency spectrum, denoted by . In this paper, we introduce two new operations and , and describe the adjacency spectra of and of regular graphs , and ...
Dijian Wang, Yaoping Hou, Zikai Tang
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