Vulnerability Parameter of Book graph

Kavitha B N; Indrani Pramod Kelkar; Rajanna K R

doi:https://doi.org/10.14445/22315373/IJMTT-V66I5P501

International Journal of Mathematics Trends and Technology

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Volume 66 | Issue 5 | Year 2020 | Article Id. IJMTT-V66I5P501 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I5P501

Vulnerability Parameter of Book graph

Kavitha B N, Indrani Pramod Kelkar, Rajanna K R

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.

Keywords

Book graph, Tenacity, Rupture degree, Vulnerability.

References

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Citation :

Kavitha B N, Indrani Pramod Kelkar, Rajanna K R, "Vulnerability Parameter of Book graph," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 5, pp. 1-5, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I5P501