About Secured Isolate Inclusive Sets in Graphs

D.K. Thakkar¹ , N.J. Savaliya²

Section:Research Paper, Product Type: Isroset-Journal
Vol.6 , Issue.1 , pp.276-281, Feb-2019

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.276281

Online published on Feb 28, 2019

Copyright © D.K. Thakkar, N.J. Savaliya . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In this paper we introduce in new concept call secured isolate inclusive sets in graphs. We also define maximum secured isolate inclusive set and we define the cardinality of a maximum secured isolate inclusive set to be the secured isolate inclusive number of the graph G. We observe that a 1-maximal isolate inclusive set cannot be a secured isolate inclusive set. We also observe that if a secured isolate inclusive set contains a pendent vertex then it is an isolate in this set. It v & u are pendent vertices which are adjacent and M is a maximum secured isolate inclusive set of G then v∈M & u∉M or u∈M & v∉M.

Key-Words / Index Term :
isolate inclusive set, maximum isolate inclusive set, 1-maximal isolate inclusive set, secured isolate inclusive set, maximum secured isolate inclusive set, maximal secured isolate inclusive set, external private neighbourhood, maximum independent set, independent number.

References :
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