Neighbor Rupture Degree of Gear Graphs

Abstract

Various structures such as communication networks, internet networks, transportation networks, etc. can be demonstrated with the aid of graphs. The common feature of these networks is the presence of one or more centers and the connection between them partially or completely. These networks can be modelled with the help of a graph showing the centers by vertices and the connections by edges. In case of a problem encountered with the centers or the connections of a network, the resistance of the network is called vulnerability. There are some graph parameters to measure the vulnerability such as connectivity, integrity, toughness, tenacity, rupture degree and neighbor rupture degree. Some of these parameters only consider vertices, some of them take into account the neighbors of the vertices. Neighbor rupture degree is a vulnerability parameter that considers the neighborhoods. In this study, the general solutions for the neighbor rupture degree of gear graphs are obtained.