Vulnerability Parameter of Book graph

**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 B_{m} is cross product of star graph S_{m+1} and path graph P_{2.} 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.