Assorted Secure and Co - Secure Domination Number of Some Torus, Fractal Networks and Honeycomb Structure Models

Abstract

Network on chips with various mesh relations proposed new architect designs on base of 3D formation. Each networks used here are of unique structures, properties, topological indices, different degrees and vary also with its extension view of dimensions. In this paper, we extract the higher degree nodes and placed as defenders to support and secure three times larger of its total number of nodes. Securing high confidential networks with few defenders is a risky factor of carry out the output. The nexus here maneuvered are with wide applications. Circuitry like Honey comb H_C (N), Honeycomb Cup H_CC (N), Honeycomb Cage H_CCA (N), Honeycomb Rhombic Torus HRoT_(N,M), Pyrene PY(N), Pyrene Torus PT(N), Silicate Triangular Fractal ST_F (N) with varieties of properties are used here. Secure, co – secure, strong secure, strong co – secure, perfect secure, perfect co – secure, perfect strong secure, perfect strong co – secure dominating sets of these networks are worked out in this paper with exact minimum cardinality. Some are related to one another and some are equal to one another and such kinds are also resulted here. Replacement of attacked defenders by its neighbor term marked as valuable part by the arrangement of unique node as co – defenders. Handed down in online games, in structural evolution of metallic glasses, to describe silica aero gels, implementation of a spoke hub distribution paradigm in computers, to reduce design complexity for communication scheme, epoxy resins for electrical insulation.