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...

A permutation graph G of a graph G (or generalized prism) is obtained by taking two disjoint copies of G and adding an arbitrary matching between the copies. For the parameters diameter, radius, average distance, connectivity and edge-connectivity, we compare the values of the parameter for G and G. In particular we show that if G has no isolates and is not 2Kk for k odd, then there exists a pe...

In this note we solve the edge-connectivity augmentation problem over symmetric parity families. It provides a solution for the minimum T-cut augmentation problem. We also extend a recent result of C. Q. Zhang [8].

In this paper we introduce a numerical invariant of digraphs which generalizes that of the number of connected components of a graph. The ao,clic disconnection ~(D) of a digraph D is the minimum number of (weakly) connected components of the subdigraphs obtained from D by deleting an acyclic set of arcs. We state some results about this invariant and compute its value for a variety of circulant...

It has been proved that sphericity testing for digraphs is an NP-complete problem. Here, we investigate sphericity of 3connected single source digraphs. We provide a new combinatorial characterization of sphericity and give a linear time algorithm for sphericity testing. Our algorithm tests whether a 3-connected single source digraph with n vertices is spherical in O(n) time.

Graphs and digraphs in this paper may have loops and multiple edges. Paths and circuits have no “repeated” vertices, and in digraphs they are directed. A transversal in a digraph D is a set of vertices T which intersects every circuit, i.e. DnT is acyclic. A packing of circuits (or packing for short) is a collection of pairwise (vertex-)disjoint circuits. The cardinality of a minimum transversa...

Gossiping is a problem of information dissemination described in a group of individuals connected by a communication network, where every individual in the network knows a unique item of information and needs to communicate it to everyone else. This communication pattern nds its main applications in the eld of interconnection networks for parallel and distributed architecture. Previous papers h...

This paper gives a shortest path algorithm for CFG (context free grammar) labeled and weighted digraphs where edge weights may be positive or negative, but negative-weight cycles are not allowed in the underlying unlabled graph. These results build directly on an algorithm of Barrett, Jacob, and Marathe [1]. In addition to many other results, they gave a shortest path algorithm for CFG labeled ...