This paper is published in Volume-3, Issue-3, 2017
Area
Mathematics
Author
U. Rajkumar
Org/Univ
PRIST University, Tamil Nadu, India
Pub. Date
14 June, 2017
Paper ID
V3I3-1542
Publisher
Keywords
Topology, Set- Indexer, Set-Graceful, Embedding and Completeness.

Citationsacebook

IEEE
U. Rajkumar. Bitopological Connected Graph, International Journal of Advance Research, Ideas and Innovations in Technology, www.IJARIIT.com.

APA
U. Rajkumar (2017). Bitopological Connected Graph. International Journal of Advance Research, Ideas and Innovations in Technology, 3(3) www.IJARIIT.com.

MLA
U. Rajkumar. "Bitopological Connected Graph." International Journal of Advance Research, Ideas and Innovations in Technology 3.3 (2017). www.IJARIIT.com.

Abstract

A graph G = (V, E) is called a bitopological graph if there exist a set X and a set-indexer f on G such that both f(V ) and f  (E) ∪  are topologies on X. The corresponding set-indexer is called a bitopological set-indexer of G. We prove the existence of bitopological set-indexer. We give a characterization of bitopological complete graphs. We define equi-bitopological graphs and establish certain results on equi-bitopological graphs. We identify certain classes of graphs, which are bitopological and define bitopological index β τ (G) of a finite graph G as the minimum cardinality of the underlying set X. We discuss about embeddingand NP-completeness problems of some classes of non-bitopological graphs.
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