Results 31 to 40 of about 41,123 (303)
On the automorphism group of a distance-regular graph [PDF]
, 2023 The motion of a graph is the minimal degree of its full automorphism group. Babai conjectured that the motion of a primitive distance-regular graph on $n$ vertices of diameter greater than two is at least $n/C$ for some universal constant $C > 0$, unless
Pyber, László, Skresanov, Saveliy V.
core +1 more source
The distance spectrum of corona and cluster of two graphs
AKCE International Journal of Graphs and Combinatorics, 2015 Let G be a connected graph with a distance matrix D. The D-eigenvalues {μ1,μ2,…,…,μp} of G are the eigenvalues of D and form the distance spectrum or D-spectrum of G.
G. Indulal, Dragan Stevanović
doaj +1 more source
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
On one infinite series of admissible intersection arrays of distance-regular graphs of diameter 5
Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2022 Background. One generalization of one known infinite series of admissible intersection arrays of a bipartite antipodal distance-regular graph is proposed for consideration.
I.T. Mukhamet'yanov
doaj +1 more source
On Subgraphs in Distance-Regular Graphs [PDF]
Journal of Algebraic Combinatorics, 1992 A graph is distance-regular when it is simple and for any two vertices at distance \(j\), the numbers of vertices adjacent to one and at distance \(j- 1\) (resp. \(j\) and \(j+1)\) of the other are constant (depending on \(j\) only). First some necessary conditions are derived for distance- regularity of the subgraph of the geodesics joining two ...
openaire +3 more sources
A Circuit Chasing Technique in a Distance-regular Graph with Triangles [PDF]
, 1993 We give an example of circuit chasing on a distance-regular graph which has triangle. In particular, we show that the number of columns (ci, ai, bi) = (2, 2a, e) in the intersection array of a distance-regular graph is at most 1, if all the preceding ...
Hiraki, Akira
core +1 more source
Distance-regularity and the spectrum of graphs [PDF]
Linear Algebra and its Applications, 1996 This paper considers the question whether a graph with the spectrum of a distance regular graph is distance regular. It has been known that the answer is affirmative if the distance regular graph has diameter not greater than 2, and that the answer is negative if the diameter is greater than 3.
openaire +4 more sources
Shilla distance-regular graphs
European Journal of Combinatorics, 2010 14 ...
Jack H. Koolen, Jongyook Park
openaire +3 more sources
On automorphisms of a distance-regular graph with intersection array {99, 84, 1; 1, 12, 99} [PDF]
, 2017 We find possible orders and fixed point subgraphs of a hypothetical distance-regular graph with intersection array {99, 84, 1; 1, 12, 99}. We show that, for a vertex-symmetric graph Γ with intersection array {99, 84, 1; 1, 12, 99}, its automorphism group
Belousov, I. N., I. N. Belousov
core +3 more sources
Addressing graph products and distance-regular graphs
Discrete Applied Mathematics, 2017 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 where one of the addresses equals $a$ and the other equals $b$.
Sebastian M. Cioaba +4 more
openaire +3 more sources