Distance Signatures of Extended and Co-extended Incidence Graphs of Affine Designs.

The distance matrix of a connected graph G , denoted by D (G) , is the matrix whose rows and columns are indexed by the vertex set V (G) such that the (v i , v j) -entry is d (v i , v j) , where v i , v j ∈ V (G). The distance signature sig (D (G)) of G is the inertia of D (G). In this paper, we determine the distance signature of the extended (co-extended) incidence graph of an affine design. Furthermore, we state that an open Graffiti conjecture is true for the extended (co-extended) incidence graphs of affine designs by investigating the lower bound of the matching number. [ABSTRACT FROM AUTHOR]