Vertex and edge expansion properties for rapid mixing

Hypergraph expanders from Cayley graphs

We present a simple mechanism, which can be randomised, for constructing sparse 3-uniform hypergraphs with strong expansion properties. These hypergraphs are constructed using Cayley graphs over Z2 and have vertex degree which is polylogarithmic in the number of vertices. Their expansion properties, which are derived from the underlying Cayley graphs, include analogues of vertex and edge expans...

Some results on vertex-edge Wiener polynomials and indices of graphs

The vertex-edge Wiener polynomials of a simple connected graph are defined based on the distances between vertices and edges of that graph. The first derivative of these polynomials at one are called the vertex-edge Wiener indices. In this paper, we express some basic properties of the first and second vertex-edge Wiener polynomials of simple connected graphs and compare the first and second ve...

On edge Co-PI indices

In this paper, at first we mention to some results related to PI and vertex Co-PI indices and then we introduce the edge versions of Co-PI indices. Then, we obtain some properties about these new indices.

Bounds for the Regularity of Edge Ideal of Vertex Decomposable and Shellable Graphs

A note on vertex-edge Wiener indices of graphs

The vertex-edge Wiener index of a simple connected graph G is defined as the sum of distances between vertices and edges of G. Two possible distances D_1(u,e|G) and D_2(u,e|G) between a vertex u and an edge e of G were considered in the literature and according to them, the corresponding vertex-edge Wiener indices W_{ve_1}(G) and W_{ve_2}(G) were introduced. In this paper, we present exact form...