Results 31 to 40 of about 59,909 (247)
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
openaire +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
openaire +3 more sources
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
core +2 more sources
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
core +7 more sources
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
core +4 more sources
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
doaj +1 more source
First-Fit coloring of Cartesian product graphs and its defining sets [PDF]
, 2016 Let the vertices of a Cartesian product graph $G\Box H$ be ordered by an ordering $\sigma$. By the First-Fit coloring of $(G\Box H, \sigma)$ we mean the vertex coloring procedure which scans the vertices according to the ordering $\sigma$ and for each ...
Zaker, Manouchehr
core +3 more sources
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
doaj +1 more source