The stability of a communication network is one of the important parameters for network designers and users. A communication network can be considered to be highly vulnerable if the destruction of a few elements cause large damage and only few members are able to communicate. In a communication network several vulnerability measures like binding number, toughness, scattering number, integrity, tenacity, edge tenacity and rupture degree are used to determine the resistance of network to the disruption after the failure of certain nodes (vertices) or communication links (edges). Domination theory also provides a model to measure the vulnerability of a graph network. The domination integrity of a simple connected graph is one such measure. Here we determine the domination integrity of square graph of path as well as the graphs obtained by composition (lexicographic product) of two paths.
Vaidya, S. K. and Shah, N. H.
Domination Integrity of Some Path Related Graphs,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 9,
2, Article 19.
Available at: https://digitalcommons.pvamu.edu/aam/vol9/iss2/19