Browsing by Subject "vulnerability parameters"

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Access status: Open Access ,
Vulnerability parameters of tensor product of complete equipartite graphs
(2013) Paulraja, P.; Sheeba Agnes, V.
Let $G_1$ and $G_2$ be two simple graphs. The tensor product of $G_1$ and $G_2$, denoted by $G_{1}\times G_{2}$, has vertex set $V(G_{1}\times G_{2})=V(G_{1})\times V(G_{2})$ and edge set $E(G_{1}\times G_{2})=\{(u_{1},v_{1})(u_{2},v_{2}):u_{1}u_{2}\in E(G_{1})\}$. In this paper, we determine vulnerability parameters such as toughness, scattering number, integrity and tenacity of the tensor product of the graphs $K_{r(s)}\times K_{m(n)}$ for $r\geq 3, m\geq 3, s\geq 1$ and $n\geq 1,$ where $K_{r(s)}$ denotes the complete $r$-partite graph in which each part has s vertices. Using the results obtained here the theorems proved in [Aygul Mamut, Elkin Vumar, <i>Vertex Vulnerability Parameters of Kronecker Products of Complete Graphs</i>, Information Processing Letters 106 (2008), 258–262] are obtained as corollaries.