On the neighbor rupture degree of gear graphs

Various systems designed for network structere are used in a majority of the technologies we use in the modern world. Some of these networks are electricity, internet, transportation, satellite etc. These networks can be modeled with the aid of graphs. It is an impoprtant issue that communication is continuous, fast and secure in these networks. In case of a problem encountered with the centers or the connections of a network, the resistance of the network is called vulnerability. To measure the vulnerability of graphs varius parameters were defined. Neighbor rupture degree is one of them. In the first section of this thesis, some known vulnerability parameters are given. In the second section, gear graphs and neighbour rupture degrees of gear graphs are emphasized. In the third section, some theorems and proofs are given about the neighbor rupture degree of the graphs obtained when cartesian product, join, sequential join operations are applied to gear graphs.