On the distance spectrum of minimal cages and associated distance biregular graphs

A (k,g)-cage is a k-regular simple graph of girth g with minimum possible number vertices. In this paper, (k,g)-cages which are Moore graphs referred as minimal (k,g)-cages. connected called distance regular (DR) if all its vertices have the same intersection array. bipartite biregular (DBR) partite set admit It known that DR and their subdivisions DBR graphs. for we give formula spectral radius in terms k g, also determine polynomials degree ?g2?, diameter graph. This polynomial gives eigenvalues when variable substituted by adjacency eigenvalues. We show d has d+1 distinct eigenvalues, partially answers problem posed [1]. prove every 2-partitioned transmission then radius. By obtain subdivision Finally full spectrum some