Abstract

The Cototal Hub Number in Graphs

Yasien Nafe Shawawreh and B. Shanmukha

Department of Mathematics, P.E.S. College of Engineering (Affiliated To University of Mysore) Mandya – 571401, Karnataka, INDIA.

DOI : http://dx.doi.org/10.29055/jcms/1142

ABSTRACT

A set 𝐻 of vertices in a graph 𝐺 is a hub set of 𝐺, if for any 𝑒,π‘£βˆˆπ‘‰(𝐺)𝐻, there is a π‘’π‘£βˆ’path with all intermediate vertices in 𝐻. A hub set 𝐻𝑐𝑑 is a cototal hub set of 𝐺 if 𝐺[𝑉(𝐺)𝐻𝑐𝑑] has no isolated vertex. The minimum cardinality of a cototal hub set is called the cototal hub number β„Žπ‘π‘‘(𝐺) of 𝐺. In this paper, we study the cototal hub and interior cototal hub numbers of 𝐺. Also some results concerning of these parameters are established. MSC: 05C40, 05C99.

Keywords :Cototal hub number, Interior cototal hub number, Hub number.

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