Results 11 to 20 of about 321,891 (280)
Transitive distance-regular graphs from linear groups $L(3,q)$, $q = 2,3,4,5$ [PDF]
Transactions on Combinatorics, 2020 In this paper we classify distance-regular graphs, including strongly regular graphs, admitting a transitive action of the linear groups $L(3,2)$, $L(3,3)$, $L(3,4)$ and $L(3,5)$ for which the rank of the permutation representation is at most 15.
Andrea Svob
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Tight Distance-Regular Graphs [PDF]
Journal of Algebraic Combinatorics, 2000 We consider a distance-regular graph $\G$ with diameter $d \ge 3$ and eigenvalues $k= _0> _1>... > _d$. We show the intersection numbers $a_1, b_1$ satisfy $$ ( _1 + {k \over a_1+1}) ( _d + {k \over a_1+1}) \ge - {ka_1b_1 \over (a_1+1)^2}. $$ We say $\G$ is {\it tight} whenever $\G$ is not bipartite, and equality holds above.
Jurišić, Aleksandar +2 more
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ON DISTANCE–REGULAR GRAPHS OF DIAMETER 3 WITH EIGENVALUE \(\theta=1\)
Ural Mathematical Journal, 2022 For a distance-regular graph \(\Gamma\) of diameter 3, the graph \(\Gamma_i\) can be strongly regular for \(i=2\) or 3. J.Kulen and co-authors found the parameters of a strongly regular graph \(\Gamma_2\) given the intersection array of the graph ...
Alexander A. Makhnev +2 more
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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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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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Al-Rafidain Journal of Computer Sciences and Mathematics, 2023 The new distance defined on a connected graph G contains of three terms: The ordinary distance between any two vertices in G, both the sum and the product of the two vertices' degrees, as this distance is more useful than the ordinary distance ...
Asmaa Aziz
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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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