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About 985 papers for “Distance-regular graph”

A Questionable Distance-Regular Graph

Rebecca Ross · 2016

Abstract In this paper, we introduce distance-regular graphs and develop the intersection algebra for these graphs which is based upon its intersection numbers. We discuss results following from the definition of the intersection algebra. We investigate two examples of distance-regular graphs and show how these results apply. Finally, we introduce parameters that determine intersection numbers. We investigate if these intersection numbers are nonnegative and feasible. 1.

Cited by 0

Automorphisms of distance-regular graph with intersection array $\{24,18,9;1,1,16\}$

A. A. Makhnëv · Sibirskie Elektronnye Matematicheskie Izvestiya · 2019

Koolen and Park classified Shilla graphs with b = 2 and with b = 3. Prime divisors of orders of automorphisms and the fixed point subgraphs of automorphisms of prime orders are studied for a hypothetical distance-regular graph with intersection array {24, 18, 9; 1, 1, 16}. Let G = Aut() is nonsolvable group, = G/S(G) and T is the socle of . Then G contains now elements of order 35 and T = J2, A10

Cited by 1Open access

The Pseudo Cosine Sequences of a Distance-Regular Graph

Arlene A. Pascasio, Paul Terwilliger · ArXiv.org · 2003

Let $G$ denote a distance-regular graph with diameter $D\ge 3$, valency $k$, and intersection numbers $a_i$, $b_i$, $c_i$. By a {\it pseudo cosine sequence} of $G$ we mean a sequence of real numbers $s_0, s_1, ..., s_D$ such that $s_0=1$ and $c_i s_{i-1}+a_i s_i+b_i s_{i+1}=k s_1 s_i$ for $ 0 \le i \le D-1$. Let $s_0, s_1,..., s_D$ and $p_0, p_1, ..., p_D$ denote pseudo cosine sequences of $G$. We say this pair of sequences is {\it tight} whenever $s_0 p_0, s_1 p_1, ..., s_D p_D$ is a pseudo cosine sequence of $G$. In this paper, we determine all the tight pairs of pseudo cosine sequences of $G$.

Cited by 0Open access