TY  - JOUR
ID  - Paulraja2013
LB  - Paulraja2013
AU  - Paulraja, P.
AU  - Sheeba Agnes, V.
TI  - Vulnerability parameters of tensor product of complete equipartite graphs
ST  - Vulnerability parameters of tensor product of complete equipartite graphs
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2013
VL  - 33
IS  - 4
SP  - 741
EP  - 750
DO  - http://dx.doi.org/10.7494/OpMath.2013.33.4.741
UR  - http://dx.doi.org/10.7494/OpMath.2013.33.4.741
AB  - 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 \(E(G_{1}\times G_{2})=\{(u_{1},v_{1})(u_{2},v_{2}):u_{1}u_{2}\in E(G_{1})\) and \(v_{1}v_{2}\in E(G_{2})\}\). 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, Vertex Vulnerability Parameters of Kronecker Products of Complete Graphs, Information Processing Letters 106 (2008), 258-262] are obtained as corollaries.
KW  - fault tolerance
KW  - tensor product
KW  - vulnerability parameters
SN  - 1232-9274
ER  -