We express the discrete Ricci curvature of a graph as minimal eigenvalue family matrices, one for each vertex whose entries depend on local adjacency structure graph. Using this method we compute or bound Cayley graphs finite Coxeter groups and affine Weyl groups. As an application obtain isoperimetric inequality that holds all

The D-eigenvalues of a graph G are the eigenvalues of its distance matrix D , and the D-energy ED(G) is the sum of the absolute values of its D-eigenvalues. Two graphs are said to be D-equienergetic if they have the same D-energy. In this note we obtain bounds for the distance spectral radius and D-energy of graphs of diameter 2. Pairs of equiregular D-equienergetic graphs of diameter 2, on p =...

In this paper, structural properties of chordal graphs are studied, establishing a relationship between these structures and integer Laplacian eigenvalues. We present the characterization with equal vertex algebraic connectivities, by means vertices that compose minimal separators graph; we stablish sufficient condition for cardinality maximal clique to appear as an eigenvalue. Finally, review ...