Results 51 to 60 of about 3,086,920 (343)

Distance-regularity and the spectrum of graphs [PDF]

Linear Algebra and its Applications, 1996
This paper considers the question whether a graph with the spectrum of a distance regular graph is distance regular. It has been known that the answer is affirmative if the distance regular graph has diameter not greater than 2, and that the answer is negative if the diameter is greater than 3.
openaire   +4 more sources

On the distance α-spectral radius of a connected graph

Journal of Inequalities and Applications, 2020
For a connected graph G and α ∈ [ 0 , 1 ) $\alpha \in [0,1)$ , the distance α-spectral radius of G is the spectral radius of the matrix D α ( G ) $D_{\alpha }(G)$ defined as D α ( G ) = α T ( G ) + ( 1 − α ) D ( G ) $D_{\alpha }(G)=\alpha T(G)+(1-\alpha )
Haiyan Guo, Bo Zhou
doaj   +1 more source

DISTANCE-REGULAR GRAPH WITH INTERSECTION ARRAY {27, 20, 7; 1, 4, 21} DOES NOT EXIST

Ural Mathematical Journal, 2020
In the class of distance-regular graphs of diameter 3 there are 5 intersection arrays of graphs with at most 28 vertices and noninteger eigenvalue. These arrays are \(\{18,14,5;1,2,14\}\), \(\{18,15,9;1,1,10\}\), \(\{21,16,10;1,2,12\}\), \(\{24,21,3;1,3 ...
Konstantin S. Efimov, Alexander A. Makhnev   +1 more
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THE VERTEX DISTANCE COMPLEMENT SPECTRUM OF SUBDIVISION VERTEX JOIN AND SUBDIVISION EDGE JOIN OF TWO REGULAR GRAPHS

Ural Mathematical Journal, 2021
The vertex distance complement (VDC) matrix \(\textit{C}\), of a connected graph  \(G\) with vertex set consisting of \(n\) vertices, is a real symmetric matrix \([c_{ij}]\) that takes the value \(n - d_{ij}\) where \(d_{ij}\) is the distance between the
Ann Susa Thomas, Sunny Joseph Kalayathankal, Joseph Varghese Kureethara   +2 more
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Distance-regular Subgraphs in a Distance-regular Graph, IV

European Journal of Combinatorics, 1995
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On Bipartite Q-Polynomial Distance-Regular Graphs with Diameter 9, 10, or 11

Electronic Journal of Combinatorics, 2018
Let $\Gamma$ denote a bipartite distance-regular graph with diameter $D$. In [Caughman (2004)], Caughman showed that if $D \ge 12$, then $\Gamma$ is $Q$-polynomial if and only if one of the following (i)-(iv) holds: (i) $\Gamma$ is the ordinary $2D ...
Štefko Miklavič
semanticscholar   +1 more source

On 14-regular distance magic graphs

Electronic Journal of Graph Theory and Applications
Let G be a graph with n vertices. By N(v) we denote the set of all vertices adjacent to v. A bijection f : V(G)→{1, 2, …, n} is a distance magic labeling of G if there exists an integer k such that the sum of labels of all vertices adjacent to v is k for
Petr Kovář, Matěj Krbeček
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Asymptotic Delsarte cliques in distance-regular graphs [PDF]

Journal of Algebraic Combinatorics, 2015
We give a new bound on the parameter λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt ...
L. Babai, John Wilmes
semanticscholar   +1 more source

On Almost Distance-Regular Graphs [PDF]

2010 Mathematics Subject Classification: 05E30, 05C50;distance-regular graph;walk-regular graph;eigenvalues;predistance ...
Fiol, M.A., Dalfo, C., Gorissen, B.L., Garriga, E., Dam, E.R. van   +4 more
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Handicap Labelings of 4-Regular Graphs

Advances in Electrical and Electronic Engineering, 2017
Let G be a simple graph, let f : V(G)→{1,2,...,|V(G)|} be a bijective mapping. The weight of v ∈ V(G) is the sum of labels of all vertices adjacent to v. We say that f is a distance magic labeling of G if the weight of every vertex is the same
Petr Kovar, Michal Kravcenko, Matej Krbecek, Adam Silber   +3 more
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