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In this article, we study Pareto eigenvalues of distance matrix of connected graphs and show that the non zero entries of every distance Pareto eigenvector of a tree forms a strictly convex function on the forest generated by the vertices corresponding to the non zero entries of the vector. Besides we find the minimum number of possible distance Pareto eigenvalue of a connected graph and establish lower bounds for $n$ largest distance Pareto eigenvalues of a connected graph of order $n.$ Finally, we discuss some bounds for the second largest distance Pareto eigenvalue and find graphs with optimal second largest distance Pareto eigenvalue., 21 pages, 4 figures

Supervisor: Bhaba Kr. Sarma, This thesis aims at filling some conspicuous gaps in the study of spectra of unicyclic graphs, and answering some recent questions on relations between the structure of a unicyclic graph and the spectrum of its adjacency matrix...