Computing The Scattering Number and The Toughness for Gear Graphs


Ersin Aslan, Alpay Kirlangic




In a communication network, the vulnerability measures the resistance of the network to disruption of operation after the failure of certain stations or communication links. To measure the vulnerability we have some parameters which are connectivity, toughness, scattering number, integrity, tenacity and their edge analogues. This paper includes several results on the toughness and the scattering number of a gear graph as a communication network. Firstly, we compute the scattering number and toughness of a gear graph. In addition, the scattering number and toughness of the complement of a gear graph, the cartesian product of two gear graphs and the sequential join of gear graphs are computed. Finally, we compare the results for the scattering number and toughness.