Results 11 to 20 of about 322,612 (279)
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'.
Dalfó Simó, Cristina +4 more
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Shilla distance-regular graphs
European Journal of Combinatorics, 2010 14 ...
Koolen, JH, Park, J
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The distance spectrum of two new operations of graphs [PDF]
Transactions on Combinatorics, 2020 Let $G$ be a connected graph with vertex set $V(G)=\{v_1, v_2,\ldots,v_n\}$. The distance matrix $D=D(G)$ of $G$ is defined so that its $(i,j)$-entry is equal to the distance $d_G(v_i,v_j)$ between the vertices $v_i$ and $v_j$ of $G$. The eigenvalues
Zikai Tang +3 more
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Arithmetic completely regular codes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2016 In this paper, we explore completely regular codes in the Hamming graphs and related graphs. Experimental evidence suggests that many completely regular codes have the property that the eigenvalues of the code are in arithmetic progression.
Jacobus Koolen +3 more
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Some Resolving Parameters in a Class of Cayley Graphs
Journal of Mathematics, 2022 Resolving parameters are a fundamental area of combinatorics with applications not only to many branches of combinatorics but also to other sciences.
Jia-Bao Liu, Ali Zafari
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ON SOME VERTEX-TRANSITIVE DISTANCE-REGULAR ANTIPODAL COVERS OF COMPLETE GRAPHS
Ural Mathematical Journal, 2022 In the present paper, we classify abelian antipodal distance-regular graphs \(\Gamma\) of diameter 3 with the following property: \((*)\) \(\Gamma\) has a transitive group of automorphisms \(\widetilde{G}\) that induces a primitive almost simple ...
Ludmila Yu. Tsiovkina
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The Generalized Distance Spectrum of the Join of Graphs [PDF]
, 2020 Let G be a simple connected graph. In this paper, we study the spectral properties of the generalized distance matrix of graphs, the convex combination of the symmetric distance matrix D(G) and diagonal matrix of the vertex transmissions Tr(G) .
Alhevaz, Abdollah +3 more
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D-magic strongly regular graphs
AKCE International Journal of Graphs and Combinatorics, 2020 For a set of distances D, a graph G on n vertices is said to be D-magic if there exists a bijection and a constant k such that for any vertex x, where is the D-neighbourhood set of x.
Rinovia Simanjuntak, Palton Anuwiksa
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Geometric aspects of 2-walk-regular graphs [PDF]
, 2013 A $t$-walk-regular graph is a graph for which the number of walks of given length between two vertices depends only on the distance between these two vertices, as long as this distance is at most $t$. Such graphs generalize distance-regular graphs and $t$
Cámara, Marc +3 more
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SHILLA GRAPHS WITH \(b=5\) AND \(b=6\)
Ural Mathematical Journal, 2021 A \(Q\)-polynomial Shilla graph with \(b = 5\) has intersection arrays \(\{105t,4(21t+1),16(t+1); 1,4 (t+1),84t\}\), \(t\in\{3,4,19\}\). The paper proves that distance-regular graphs with these intersection arrays do not exist.
Alexander A. Makhnev, Ivan N. Belousov
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