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Distance-regular graphs with a few q-distance eigenvalues [PDF]
Discrete MathematicsIn this paper we study when the $q$-distance matrix of a distance-regular graph has few distinct eigenvalues. We mainly concentrate on diameter 3.
Mamoon Abdullah +3 more
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Addressing graph products and distance-regular graphs [PDF]
Discrete Applied Mathematics, 2016 Graham and Pollak showed that the vertices of any connected graph $G$ can be assigned $t$-tuples with entries in $\{0, a, b\}$, called addresses, such that the distance in $G$ between any two vertices equals the number of positions in their addresses ...
S. Cioabă +4 more
semanticscholar +5 more sources
The Electronic Journal of Combinatorics, 2014 This is a survey of distance-regular graphs. We present an introduction to distance-regular graphs for the reader who is unfamiliar with the subject, and then give an overview of some developments in the area of distance-regular graphs since the ...
E. V. van Dam, J. Koolen, Hajime Tanaka
semanticscholar +5 more sources
On almost distance-regular graphs [PDF]
Journal of Combinatorial Theory - Series A, 2011 Distance-regular graphs are a key concept in Algebraic Combinatorics and have given rise to several generalizations, such as association schemes. Motivated by spectral and other algebraic characterizations of distance-regular graphs, we study `almost distance-regular graphs'.
Cristina Dalfó, E Garriga, M A Fiol
exaly +11 more sources
On the coset graph construction of distance-regular graphs
Discrete Mathematics, 2022 We show that no more new distance-regular graphs in the tables of the book of (Brouwer, Cohen, Neumaier, 1989) can be produced by using the coset graph of additive completely regular codes over finite fields.
Patrick Sole +2 more
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Nonexistence of a Class of Distance-Regular Graphs
The Electronic Journal of Combinatorics, 2015 Let $\Gamma$ denote a distance-regular graph with diameter $D \geq 3$ and intersection numbers $a_1=0, a_2 \neq 0$, and $c_2=1$. We show a connection between the $d$-bounded property and the nonexistence of parallelograms of any length up to $d+1 ...
Yu-pei Huang +2 more
semanticscholar +4 more sources
m-Distance-regular graphs and their relation to multivariate P-polynomial association schemes [PDF]
Discrete Mathematics, 2023 An association scheme is $P$-polynomial if and only if it consists of the distance matrices of a distance-regular graph. Recently, bivariate $P$-polynomial association schemes of type $(\alpha,\beta)$ were introduced by Bernard et al., and multivariate ...
Pierre-Antoine Bernard +4 more
semanticscholar +1 more source
A valency bound for distance-regular graphs
Journal of Combinatorial Theory - Series A, 2018 Zhi Qiao, Jack Koolen
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POSITIVITY OF GIBBS STATES ON DISTANCE-REGULAR GRAPHS [PDF]
Infinite Dimensional Analysis Quantum Probability and Related Topics, 2021 We study criteria which ensure that Gibbs states (often also called generalized vacuum states) on distance-regular graphs are positive. Our main criterion assumes that the graph can be embedded into a growing family of distance-regular graphs.
M. Voit
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On distance labelings of 2-regular graphs
Electronic Journal of Graph Theory and Applications, 2021 Let G be a graph with |V(G)| vertices and ψ : V(G) → {1, 2, 3, ... , |V(G)|} be a bijective function. The weight of a vertex v ∈ V(G) under ψ is wψ(v) = ∑u ∈ N(v)ψ(u). The function ψ is called a distance magic labeling of G, if wψ(v) is a constant for
Anak Agung Gede Ngurah +1 more
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