Results 31 to 40 of about 14,964 (295)
Optimal Adjacency Labels for Subgraphs of Cartesian Products [PDF]
, 2022 For any hereditary graph class $F$, we construct optimal adjacency labeling schemes for the classes of subgraphs and induced subgraphs of Cartesian products of graphs in $F$.
Zamaraev, Viktor +5 more
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The Cartesian product of graphs with loops
Ars Mathematica Contemporanea, 2015 We extend the definition of the Cartesian product to graphs with loops and show that the Sabidussi-Vizing unique factorization theorem for connected finite simple graphs still holds in this context for all connected finite graphs with at least one unlooped vertex. We also prove that this factorization can be computed in O(m) time, where m is the number
Tetiana Boiko +4 more
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Distance Magic Cartesian Products of Graphs
Discussiones Mathematicae Graph Theory, 2016 A distance magic labeling of a graph G = (V,E) with |V | = n is a bijection ℓ : V → {1, . . . , n} such that the weight of every vertex v, computed as the sum of the labels on the vertices in the open neighborhood of v, is a constant.
Cichacz Sylwia +3 more
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On the Crossing Numbers of Cartesian Products of Stars and Graphs of Order Six
Discussiones Mathematicae Graph Theory, 2013 The crossing number cr(G) of a graph G is the minimal number of crossings over all drawings of G in the plane. According to their special structure, the class of Cartesian products of two graphs is one of few graph classes for which some exact values of ...
Klešč Marián, Schrötter Štefan
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On the Width of the Cartesian Product of Ordinals
Order, 2022 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Oriented Chromatic Number of Cartesian Products Pm □ Pn and Cm □ Pn
Discussiones Mathematicae Graph Theory, 2022 We consider oriented chromatic number of Cartesian products of two paths Pm □ Pn and of Cartesian products of paths and cycles, Cm □ Pn. We say that the oriented graph G→\vec G is colored by an oriented graph H→\vec H if there is a homomorphism from G ...
Nenca Anna
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On Cartesian Products of Orthogonal Double Covers
International Journal of Mathematics and Mathematical Sciences, 2013 Let H be a graph on n vertices and 𝒢 a collection of n subgraphs of H, one for each vertex, where 𝒢 is an orthogonal double cover (ODC) of H if every edge of H occurs in exactly two members of 𝒢 and any two members share an edge whenever the ...
R. El Shanawany, M. Higazy, A. El Mesady
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The metric dimension of circulant graphs and their Cartesian products [PDF]
Opuscula Mathematica, 2017 Let \(G=(V,E)\) be a connected graph (or hypergraph) and let \(d(x,y)\) denote the distance between vertices \(x,y\in V(G)\). A subset \(W\subseteq V(G)\) is called a resolving set for \(G\) if for every pair of distinct vertices \(x,y\in V(G)\), there ...
Kevin Chau, Shonda Gosselin
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Oriented Chromatic Number of Cartesian Products and Strong Products of Paths
Discussiones Mathematicae Graph Theory, 2019 An oriented coloring of an oriented graph G is a homomorphism from G to H such that H is without selfloops and arcs in opposite directions. We shall say that H is a coloring graph.
Dybizbański Janusz, Nenca Anna
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(Open) packing number of some graph products [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 The packing number of a graph $G$ is the maximum number of closed neighborhoods of vertices in $G$ with pairwise empty intersections. Similarly, the open packing number of $G$ is the maximum number of open neighborhoods in $G$ with pairwise empty ...
Doost Ali Mojdeh +3 more
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