if we think of the graph as modeling a network, the vulnerability measure the resistance of the network to disruption of operation after the failure of certain stations or communication links. many graph theoretical parameters have been used to describe the vulnerability of communication networks, including connectivity, integrity, toughness, binding number and tenacity.in this paper we discuss...

If we think of the graph as modeling a network, the vulnerability measure the resistance of the network to disruption of operation after the failure of certain stations or communication links. Many graph theoretical parameters have been used to describe the vulnerability of communication networks, including connectivity, integrity, toughness, binding number and tenacity.In this paper we discuss...

Distance-balanced graphs are introduced as graphs in which every edge uv has the following property: the number of vertices closer to u than to v is equal to the number of vertices closer to v than to u. Basic properties of these graphs are obtained. In this paper, we study the conditions under which some graph operations produce a distance-balanced graph.

In this paper, we first collect the earlier results about some graph operations and then we present applications of these results in working with chemical graphs.

Our goal is to prove a generating theorem for the class E5 of all 5-regular simple planar graphs. This is a progress report. First, we will see the general information from Euler’s formula and the Discharge Method. Second, the basic graph operation D-operation will be introduced. Third, there are two cases to be discussed separately. A graph either contains an edge that is a part of three disti...