History and Recent Developments of Distance Spectral Radius

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Combinatorial matrix theory is a branch of algebraic graph theory, that studies by and large, the interrelations between linear algebra and graph theory. The investigation on the spectral radius of graphs is an important topic in the theory of graph spectra. Primarily, this book contains a survey (and some recent developments) on the largest eigenvalue of the distance matrix of a graph and its relation to the structure of the graph. In literature, extensive study has been made on Adjacency and Laplacian matrices. The distance matrix of a graph, while not as common as the more familiar adjacency matrix, has nevertheless come up in several different areas, including communication network design and network flow algorithms. We hope that this book will ignite the young minds to carry out a research in this fruitful domain and will fill some conspicuous gaps in the study of distance spectra of graphs.

Somnath Paul received his PhD in Mathematical Sciences from Tezpur University. After serving as an Assistant Professor at NIT Silchar for a semester, he joined Tezpur University. Currently he is working as an Assistant Professor (on contract) at Tezpur University. His research interest lie in the field of Spectral Graph Theory.