Results 31 to 40 of about 3,086,920 (343)

Distance-regular graphs with diameter 3 and eigenvalue a2 − c3

, 2020
In this paper, we consider the distance-regular graphs Γ whose distance-2 graphs Γ 2 are strongly regular. Note that if Γ is bipartite, then its distance-2 graph is not connected.
Quaid Iqbal, J. Koolen, Jongyook Park, M. Ur Rehman   +3 more
semanticscholar   +1 more source

Two distance-regular graphs [PDF]

Journal of Algebraic Combinatorics, 2011
We construct two families of distance-regular graphs, namely the subgraph of the dual polar graph of type B_3(q) induced on the vertices far from a fixed point, and the subgraph of the dual polar graph of type D_4(q) induced on the vertices far from a fixed edge. The latter is the extended bipartite double of the former.
Brouwer, Andries E., Pasechnik, Dmitrii V.   +1 more
openaire   +5 more sources

On some distance-regular graphs with many vertices [PDF]

Journal of Algebraic Combinatorics, 2018
We construct distance-regular graphs, including strongly regular graphs, admitting a transitive action of the Chevalley groups $$G_2(4)$$ G 2 ( 4 ) and $$G_2(5)$$ G 2 ( 5 ) , the orthogonal group O (7, 3) and the Tits group $$T=$$ T = $$^2F_4(2)'$$ 2 F 4
Dean Crnković, S. Rukavina, Andrea Švob   +2 more
semanticscholar   +1 more source

Weakly distance-regular digraphs whose underlying graphs are distance-regular, I [PDF]

Journal of Algebraic Combinatorics, 2023
Weakly distance-regular digraphs are a natural directed version of distance-regular graphs. In Wang and Suzuki (Discrete Math 264:225–236, 2003), the third author and Suzuki proposed a question when an orientation of a distance-regular graph defines a ...
Yuefeng Yang, Qing-Yi Zeng, Kai-Shun Wang   +2 more
semanticscholar   +1 more source

Tight Distance-Regular Graphs [PDF]

Journal of Algebraic Combinatorics, 2000
We consider a distance-regular graph $\G$ with diameter $d \ge 3$ and eigenvalues $k=θ_0>θ_1>... >θ_d$. We show the intersection numbers $a_1, b_1$ satisfy $$ (θ_1 + {k \over a_1+1}) (θ_d + {k \over a_1+1}) \ge - {ka_1b_1 \over (a_1+1)^2}. $$ We say $\G$ is {\it tight} whenever $\G$ is not bipartite, and equality holds above.
Jurišić, Aleksandar, Koolen, Jack, Terwilliger, Paul   +2 more
openaire   +2 more sources

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
doaj   +1 more source

Edge-distance-regular graphs are distance-regular

Journal of Combinatorial Theory, Series A, 2013
A graph is edge-distance-regular when it is distance-regular around each of its edges and it has the same intersection numbers for any edge taken as a root. In this paper we give some (combinatorial and algebraic) proofs of the fact that every edge-distance-regular graph $\G$ is distance-regular and homogeneous.
Cámara Vallejo, Marc, Dalfó Simó, Cristina, Delorme, Charles, Fiol Mora, Miquel Àngel, Suzuki, Hiroshi   +4 more
openaire   +4 more sources

Characterizing Distance-Regularity of Graphs by the Spectrum [PDF]

Journal of Combinatorial Theory, Series A, 2005
We characterize the distance-regular Ivanov-Ivanov-Faradjev graph from the spectrum, and construct cospectral graphs of the Johnson graphs, Doubled Odd graphs, Grassmann graphs, Doubled Grassmann graphs, antipodal covers of complete bipartite graphs, and many of the Taylor graphs.We survey the known results on cospectral graphs of the Hamming graphs ...
Edwin R. van Dam, Willem H. Haemers, Jacobus H. Koolen, Edward Spence   +3 more
openaire   +9 more sources

AUTOMORPHISMS OF DISTANCE-REGULAR GRAPH WITH INTERSECTION ARRAY {39; 36; 4; 1; 1; 36}

Ural Mathematical Journal, 2018
Makhnev and Nirova have found intersection arrays of distance-regular graphs with no more than \(4096\) vertices, in which \(\lambda=2\)  and \(\mu=1\). They proposed the program of investigation of distance-regular graphs with \(\lambda=2\) and \(\mu=1\)
Konstantin S. Efimov, Aleksandr A. Makhnev   +1 more
doaj   +1 more source

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
doaj   +1 more source