Neighbor Rupture Degree of Gear Graphs

Year 2017, Volume: 13 Issue: 2, 319 - 323, 30.06.2017

Gökşen Bacak Turan Emre Demirtekin

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.

Keywords

Gear graph, generalized gear graph, graph theory, neighbour rupture degree, vulnerability

References

• M.T. Rahim, M. Farooq, M.Ali and S.Jan, Multi-level distance labelings for generalized gear graphs, International Journal of Mathematics and Soft Computing, Vol.2 No.1 (2012), 57-63.