Integrity of Generalized Transformation Graphs

Bommanahal Basavanagoud, Shruti Policepatil

Abstract


The values of vulnerability helps the network designers to construct such a communication network which remains stable after some of its nodes or communication links are damaged. The transformation graphs considered in this paper are taken as model of the network system and it reveals that, how network can be made more stable and strong. For this purpose the new nodes are inserted in the network. This construction of new network is done by using the definition of generalized transformation graphs of a graphs. Integrity is one of the best vulnerability parameter.
In this paper, we investigate the integrity of generalized transformation graphs and their complements. Also, we find integrity of semitotal point graph of combinations of basic graphs. Finally, we characterize few graphs having equal integrity values as that of generalized transformation graphs of same structured graphs.


Keywords


Vulnerability; connectivity; integrity; generalized transformation graphs; semitotal point graph

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References


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DOI: http://dx.doi.org/10.23755/rm.v40i1.576

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Copyright (c) 2021 Shruti Policepatil, B. Basavanagoud

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Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.