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(vi,vj)-entry is d(vi,vj),where vi,vj∈V(G).The distance signature sig(D(G...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(vi,vj)-entry is d(vi,vj),where vi,vj∈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.展开更多
基金supported by the National Natural Science Foundation of China(12271311,12101410,12201414)Taishan Scholars Program of Shandong Province.
文摘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(vi,vj)-entry is d(vi,vj),where vi,vj∈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.
