• P.PRIYANKA
• B.AMRINTAJ
• V.PRIYADHARSHINI
• V.ANGESHWARI
• N.ALIMA

The connectivity of a graph is an important measurement for the fault-tolerance of the network. To provide more accurate measures for the fault –tolerance of networks than the connectivity some generalizations connectivity have been introduced. The study of n-dimensional hyper cubes can be embedded with (n-1-f). Mutually independent Hamiltonian cycles when f≤n-2 faulty edges. The connectivity of a network the minimum number of nodes whose removal will disconnect the network is directly related to its reliability and fault tolerability hence an important indicator of the networks robustness. We extend the notion of connectivity by introducing two new kinds of connectivity called structure connectivity and substructure connectivity.

Structure connectivity, cycles, hypercubes, interconnection network, fault tolareance, hamiltational cycle, substructure connectivity, hamiltation, pancake network, star network

"CONNECTIVITY AND HAMILTONIAN GRAPH", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.9, Issue 8, page no.b417-b424, August-2022, Available :http://www.jetir.org/papers/JETIR2208154.pdf

"CONNECTIVITY AND HAMILTONIAN GRAPH", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.9, Issue 8, page no. ppb417-b424, August-2022, Available at : http://www.jetir.org/papers/JETIR2208154.pdf