Distance Matrices and Spectral Radii of Graphs

Distance matrix of a graph is a symmetric matrix which encodes distances between all pairs of verticesin the graph. in 1971, graham and pollack showed that the so-called addressing problem in data communication systems is related to the number of negative eigenvalues of the distance matrix. they alsoshowed that the determinant of the distance matrix of a tree depends only on the number of its vertices.since then, this topic has been an active area of research, and its combinatorial and spectral aspects havebeen extensively studied. after giving a brief overview of the subject, i will discuss some recent extremalproblems regarding the distance spectral radius, that is, the largest eigenvalue of the distance matrix. iwill also present our recent extremal results on the distance spectral radius of bicyclic graphs.