We study the family of p-resistances on graphs for p ≥ 1. This family generalizes the standard resistance distance. We prove that for any fixed graph, for p = 1 the p-resistance coincides with the shortest path distance, for p = 2 it coincides with the standard resistance distance, and for p → ∞ it converges to the inverse of the minimal s-t-cut in the graph. Secondly, we consider the special c...

Let [Formula: see text] be a simple graph. The resistance distance between [Formula: see text], denoted by [Formula: see text], is defined as the net effective resistance between nodes i and j in the corresponding electrical network constructed from G by replacing each edge of G with a resistor of 1 Ohm. The resistance-distance matrix of G, denoted by [Formula: see text], is a [Formula: see tex...

mathematical chemistry is a branch of theoretical chemistry for discussion and prediction of the molecular structure using mathematical methods without necessarily referring to quantum mechanics. in theoretical chemistry, distance-based molecular structure descriptors are used for modeling physical, pharmacologic, biological and other properties of chemical compounds. the wiener polarity index ...

We present a method to find outliers using ‘commute distance’ computed from a random walk on graph. Unlike Euclidean distance, commute distance between two nodes captures both the distance between them and their local neighborhood densities. Indeed commute distance is the Euclidean distance in the space spanned by eigenvectors of the graph Laplacian matrix. We show by analysis and experiments t...

The chromatic number of a graph G, denoted by χ(G), is the minimum number of colors such that G can be colored with these colors in such a way that no two adjacent vertices have the same color. A clique in a graph is a set of mutually adjacent vertices. The maximum size of a clique in a graph G is called the clique number of G. The Turán graph Tn(k) is a complete k-partite graph whose partition...