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 …

The k th power of a graph G=(V, E), G k, is the graph whose vertex set is V and in which two
distinct vertices are adjacent if and only if their distance in G is at most k. This article proves …

The k-independence number of a graph is the maximum size of a set of vertices at pairwise
distance greater than k. A graph is called k-partially walk-regular if the number of closed …

A weighted (unweighted) graph G is called equiarboreal if the sum of weights (the number)
of spanning trees containing a given edge in G is independent of the choice of edge. In this …

In this paper, we will classify the 2-partially distance-regular graphs whose each local graph
has second largest eigenvalue at most one. As an application, we classify the 2-walk-regular …

We study bipartite distance-regular Cayley graphs with diameter three or four. We give
sufficient conditions under which a bipartite Cayley graph can be constructed on the …

In order to obtain perfect state transfer between two sites in a network of interacting qubits,
their corresponding vertices in the underlying graph must satisfy a combinatorial property …

In this paper we consider the concept of preintersection numbers of a graph. These numbers
are determined by the spectrum of the adjacency matrix of the graph, and generalize the …

The spanning tree packing number of a graph G is the maximum number of edge-disjoint
spanning trees in G, and the arboricity of G is the minimum number of edge-disjoint forests …

In this paper, we look at distance-regular graphs with induced subgraphs K r, t, where 1≤
r≤ t are integers. In particular, we show that if a distance-regular graph Γ with diameter D≥ …