Results 11 to 20 of about 41,123 (303)

Edge-distance-regular graphs [PDF]

Journal of Combinatorial Theory, Series A, 2011
Edge-distance-regularity is a concept recently introduced by the authors which is similar to that of distance-regularity, but now the graph is seen from each of its edges instead of from its vertices. More precisely, a graph Γ with adjacency matrix A is edge-distance-regular when it is distance-regular around each of its edges and with the same ...
Cámara Vallejo, Marc, Dalfó Simó, Cristina, Fàbrega Canudas, José, Fiol Mora, Miquel Àngel, Garriga Valle, Ernest   +4 more
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ON A CLASS OF EDGE-TRANSITIVE DISTANCE-REGULAR ANTIPODAL COVERS OF COMPLETE GRAPHS

Ural Mathematical Journal, 2021
The paper is devoted to the problem of classification of edge-transitive distance-regular antipodal covers of complete graphs. This extends the classification of those covers that are arc-transitive, which has been settled except for some tricky cases ...
Ludmila Yu. Tsiovkina
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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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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
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NEW BOUNDS AND EXTREMAL GRAPHS FOR DISTANCE SIGNLESS LAPLACIAN SPECTRAL RADIUS [PDF]

Journal of Algebraic Systems, 2021
The distance signless Laplacian spectral radius of a connected graph $G$ is the largest eigenvalue of the distance signless Laplacian matrix of $G$, defined as $D^{Q}(G)=Tr(G)+D(G)$, where $D(G)$ is the distance matrix of $G$ and $Tr(G)$ is the diagonal ...
A. Alhevaz, M. Baghipur, S. Paul
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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 $k=θ_0>θ_1>... >θ_d$. 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
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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.
Minjia Shi, Denis S. Krotov, Patrick Solé   +2 more
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AUTOMORPHISMS OF DISTANCE-REGULAR GRAPH WITH INTERSECTION ARRAY {25; 16; 1; 1; 8; 25}

Ural Mathematical Journal, 2017
Makhnev and Samoilenko have found parameters of strongly regular graphs with no more than 1000 vertices, which may be neighborhoods of vertices in antipodal distance-regular graph of diameter 3 and with  \(\lambda=\mu\).
Konstantin S. Efimov, Alexander A. Makhnev   +1 more
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Distance-Regular Graphs

The Electronic Journal of Combinatorics, 2016
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 monograph 'BCN' [Brouwer, A.E., Cohen, A.M., Neumaier, A., Distance-Regular Graphs, Springer-Verlag, Berlin,
Edwin R. van Dam, Jack H. Koolen, Hajime Tanaka   +2 more
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Orientable -distance magic regular graphs

AKCE International Journal of Graphs and Combinatorics, 2021
Hefetz, Mütze, and Schwartz conjectured that every connected undirected graph admits an antimagic orientation (Hefetz et al., 2010). In this paper we support the analogous question for distance magic labeling. Let be an Abelian group of order .
Paweł Dyrlaga, Karolina Szopa
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