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Regular Graphs,cy matrix of a block graph. The line graph of a tree is a block graph. Some basic properties of the signless Laplacian are proved. The eigenvalues of the line graph of a tree and those of the Laplacian as well as the signless Laplacian are shown to be related to each other. This connection is exploi

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Line Graph of a Tree,degree of connectivity of the graph. We first prove basic properties of algebraic connectivity and the associated eigenvector, known as Fiedler vector. A classification of trees into two types, based on the Fiedler vector, is described. Some monotonocity properties of the coordinators of the Fiedler

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Algebraic Connectivity,tices and not on the structure of the tree. An extension of the result to graphs, due to Graham, Hoffman and Hosoya, is proved next. It asserts that the determinant of the distance matrix of a graph depends only on the blocks, and not on the way in which the blocks are joined. We then prove results

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Distance Matrix of a Tree,d is also not tractable mathematically. The resistance distance between two vertices is defined to be the effective resistance between the vertices, when the graph is viewed as an electrical network, with a unit resistance along each edge. We begin by giving an equivalent definition in terms of gene

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