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Bicyclic graphs are connected graphs in which the number of edges equals the number of vertices plus one. The class of bicyclic graphs of order n, denoted by Bn, can be partitioned into two subclasses: the class B*n of graphs which contain induced co-graphs, and the class B**n of graphs which contain induced θ-graphs. Bose et al. [2] have found the graph having the minimal distance spectral radius in B*n. In this paper, we determine the graphs having the minimal distance spectral radius in B**n. These results together give a complete characterization of the graphs having the minimal distance spectral radius in Bn. [ABSTRACT FROM AUTHOR]

We characterize graphs with minimal distance spectral radius in two classes of graphs: with vertex connectivity k and minimum degree at least k, and with given number of blocks. Moreover, we determine the unique graph that maximizes the distance spectral radius among all graphs with given clique number. [ABSTRACT FROM AUTHOR]

Trees are very common in the theory and applications of combinatorics. In this paper, we consider graphs whose underlying structure is a tree and study the behavior of the distance spectral radius under a graph transformation. As an application, we find the corona tree that maximizes the distance spectral radius among all corona trees with a fixed maximum degree. We also find the graph with minimal (maximal) distance spectral radius among all corona trees. Finally, we determine the graph with minimal distance spectral radius in a special class of corona trees. [ABSTRACT FROM AUTHOR]

In this article, we prove that among trees onnvertices and matching numberm, the dumbbellis the unique tree that maximizes the distance spectral radius, which was conjectured by Aleksandar Ilić [Distance spectral radius of trees with given matching number, Discr. Appl. Math. 158 (2010), pp. 1799–1806]. In addition, we find the unique tree that maximizes the distance spectral radius in the class of trees with a given number of pendent vertices. [ABSTRACT FROM AUTHOR]

Abstract: A cactus is a connected graph in which any two cycles have at most one common vertex. In this article, we determine the unique graph with minimal distance spectral radius in the class of all cacti with n vertices and k cycles. Also, we determine the unique graph with minimal distance spectral radius in the class of all cacti with n vertices and r pendent vertices. Moreover, we determine the class of cacti in which the maximal distance spectral radius among all cacti with n vertices and k cycles is attained. [Copyright &y& Elsevier]

Abstract: In this paper, we determine the unique graph with minimum distance spectral radius among all connected bipartite graphs of order with a given matching number. Moreover, we characterize the graphs with minimal distance spectral radius in the class of all connected bipartite graphs with a given vertex connectivity. [Copyright &y& Elsevier]

Abstract: Let be the class of all connected graphs of order with pendent vertices. In this paper, we determine the unique graph with minimal distance spectral radius in In addition, we determine the unique graph with maximal distance spectral radius in for each [Copyright &y& Elsevier]