International Conference on Linear Algebra and its Applications

The distance matrix of a simple graph G is D(G) = (di,j), where di,j is the distance between the ith and jth vertices of G. The greatest eigenvalue λ1 of D(G) is called the distance spectral radius of the graph G and is denoted by λ1(G). A simple connected graph G is called a 2-partite distance regular graph if there exists a partition V1 ∪V2 of the vertex set of G such that for i = 1, 2 and any vertex x ∈ Vi, ∑ y∈Vi d(x, y) and ∑ y∈V c i d(x, y) are constants, where V c i is the set complement of Vi. In this paper we find the exact value of the distance spectral radius of 2-partite distance regular graphs. Applying this result we find the distance spectral radius of the wheel graph Wn and the generalized Petersen graphs P (n, k) with k = 2 and 3.