Results 41 to 50 of about 59,758 (255)
On the Gonality of Cartesian Products of Graphs [PDF]
The Electronic Journal of Combinatorics, 2020 In this paper we provide the first systematic treatment of Cartesian products of graphs and their divisorial gonality, which is a tropical version of the gonality of an algebraic curve defined in terms of chip-firing. We prove an upper bound on the gonality of the Cartesian product of any two graphs, and determine instances where this bound holds with
Aidun, Ivan, Morrison, Ralph
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Hypercellular graphs: partial cubes without $Q_3^-$ as partial cube minor [PDF]
, 2019 We investigate the structure of isometric subgraphs of hypercubes (i.e., partial cubes) which do not contain finite convex subgraphs contractible to the 3-cube minus one vertex $Q^-_3$ (here contraction means contracting the edges corresponding to the ...
Chepoi, Victor +2 more
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Connectivity of Cartesian product graphs
Discrete Mathematics, 2006 Let \(n(G)\), \(\kappa(G)\), \(\lambda(G)\) and \(\delta(G)\) be the order, connectivity, edge-connectivity and minimum degree of a (di-)graph, respectively. In addition, let \(G_1\times G_2\) be the Cartesian product of two (di-)graphs \(G_1\) and \(G_2\). If \(G_1,G_2\) are two connected graphs, then the authors prove that \(\kappa(G_1\times G_2)\geq\
Xu, Jun-Ming, Yang, Chao
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Fast Recognition of Partial Star Products and Quasi Cartesian Products [PDF]
, 2013 This paper is concerned with the fast computation of a relation $\R$ on the edge set of connected graphs that plays a decisive role in the recognition of approximate Cartesian products, the weak reconstruction of Cartesian products, and the recognition ...
Hellmuth, Marc +2 more
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International Journal of Robust and Nonlinear Control, EarlyView., 2023 Abstract We propose a hierarchical energy management scheme for aggregating Distributed Energy Resources (DERs) for grid flexibility services. To prevent a direct participation of numerous prosumers in the wholesale electricity market, aggregators, as self‐interest agents in our scheme, incentivize prosumers to provide flexibility. We firstly model the
Xiupeng Chen +3 more
wiley +1 more source
Polytopality and Cartesian products of graphs [PDF]
, 2010 We study the question of polytopality of graphs: when is a given graph the graph of a polytope? We first review the known necessary conditions for a graph to be polytopal, and we provide several families of graphs which satisfy all these conditions, but ...
B. Grünbaum +20 more
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The Crossing Numbers of Products of Path with Graphs of Order Six
Discussiones Mathematicae Graph Theory, 2013 The crossing numbers of Cartesian products of paths, cycles or stars with all graphs of order at most four are known. For the path Pn of length n, the crossing numbers of Cartesian products G⃞Pn for all connected graphs G on five vertices are also known.
Klešč Marián, Petrillová Jana
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k-tuple colorings of the Cartesian product of graphs [PDF]
, 2017 A k-tuple coloring of a graph G assigns a set of k colors to each vertex of G such that if two vertices are adjacent, the corresponding sets of colors are disjoint.
Bonomo, Flavia +3 more
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Distance antimagic labelings of Cartesian product of graphs
AKCE International Journal of Graphs and Combinatorics, 2020 Let be a graph of order n. Let be a bijection. The weight w(v) of a vertex v with respect to the labeling f is defined by where N(v) is the open neighborhood of v. The labeling f is called a distance antimagic labeling if for any two distinct vertices v1,
Nancy Jaseintha Cutinho +2 more
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A New Framework to Approach Vizing’s Conjecture
Discussiones Mathematicae Graph Theory, 2021 We introduce a new setting for dealing with the problem of the domination number of the Cartesian product of graphs related to Vizing’s conjecture. The new framework unifies two different approaches to the conjecture.
Brešar Boštjan +4 more
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