Vulnerability Parameter of Book graph

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2020 by IJMTT Journal
Volume-66 Issue-5
Year of Publication : 2020
Authors : Kavitha B N, Indrani Pramod Kelkar, Rajanna K R
  10.14445/22315373/IJMTT-V66I5P501

MLA

MLA Style:Kavitha B N, Indrani Pramod Kelkar, Rajanna K R  "Vulnerability Parameter of Book graph" International Journal of Mathematics Trends and Technology 66.4 (2020):1-5. 

APA Style: Kavitha B N, Indrani Pramod Kelkar, Rajanna K R(2020). Vulnerability Parameter of Book graph International Journal of Mathematics Trends and Technology, 1-5.

Abstract
Book graph Bm is cross product of star graph Sm+1 and path graph P2. Tenacity of an incomplete connected graph G is defined as T(G) = min { |s|+m(G-s)/ w(G-s) :s ⊂ V(G), w(G-S) > 1}. where w(G-S) is the number of components in G - S. Rupture degree of graph is defined as R(G) = max{ w(G-X) - |X| - m(G-X): X ⊂ V(G) and w (G-X) >1}. Tenacity and Rupture degree are vulnerability majors of graph, which reflects on the difficulty in breaking down the network.

In this paper we present results on Tenacity and Rupture degree of Book graph. We also present relation between tenacity and rupture degree with other parameters like integrity, toughness, scattering number of book graph.

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Keywords
Book graph, Tenacity, Rupture degree, Vulnerability.