… Let be a distance-regular graph with l(1, a1 , b1) 1 and cs … We show the existence of a
certain distance-regular graph of diameter s , containing given two vertices at distance s , as …

… Then a strongly closed subgraph of diameterr +1 ≥ 3 is the collinearity graph of a Moore
geometry with valency 1 + ar+1. Thus (a1, ar+1) = (0, 1). (See [2, Theorem 6.8.1].) …

… study distance-regular subgraphs of distance-regular graphs. In … the graph induced by the
geodesies between two vertices is … third section we show that the only distance-regular graphs …

… in distanceregular graphs and this parrt conta.ins Chapters 2, 3, … representations of
distance-regular graphs and this part … stttdy distance-regular subgraphs of distance-regular …

… a distance-regular graph with diameter D 3 and distance function . A (vertex) subgraph ‘X is
… . In Section 3, we review the definition of distance-regular graphs with classical parameters (…

… subgraph in [19–21]. Let Γ be a distance-regular graph of diameter d ≥ 3 and valency k ≥
3. … section Γ denotes a distance-regular graph of diameter d ≥ 3, valency k ≥ 3, c2 > 1 and …

… on a distance-regular graph from the investigation of its ‘local structures’. In fact we have found
‘nice’ subgraphs … In Section 3, we give a sufficient condition for (CR). As an application we …

… regular connected subgraph in a distance-regular graph, … distance-regular graph with
diameter D 2. Let denote a regular connected subgraph of q, and let d : d be as in De®nition 4.1(iii…

… We show the existence of a Moore graph of diameter r + 1 and valency a,+a + 1 as a
subgraph in F. In particular, we show that either a,÷~ ffi 1 or r = 1. … In the subsequent paper [6] …

… In this paper we examine those distance regular graphs which can be embedded
isomorphically as subgraphs of … 3 is an exampie of a vertex transitive but not distance regular …