On Arc Minimal Directed Graph of Diameter Two.

Date of Submission

December 2017

Date of Award

Winter 12-12-2018

Institute Name (Publisher)

Indian Statistical Institute

Document Type

Master's Dissertation

Degree Name

Master of Technology

Subject Name

Computer Science


Advance Computing and Microelectronics Unit (ACMU-Kolkata)


Das, Sandip (ACMU-Kolkata; ISI)

Abstract (Summary of the Work)

The weak distance →d w(u, v) between any two vertices u and v→G is the shortest directed path connecting u and v. The weak diameter of an oriented graph →G diamw(→G)= max{d(u, v)|u, v ∈ V (→G)}. We denote fw(n) as the minimum arcs that an n vertex oriented graph required to be in a weak diameter two. And oclique is an oriented graph with weak diameter at most 2.In this thesis, we have settled an unknown question about fw(n) being piecewise increasing which was previously known to be asymptotically increasing, improved the previous best upper bound of fw(n). In the domain of the planar ocliques we have characterised the minimal planar ocliques showing the possible effects of removing arcs from it, and have shown some possible applications of these effects


ProQuest Collection ID: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:28843390

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Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.



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