Opuscula Math. 33, no. 4 (2013), 741-750
http://dx.doi.org/10.7494/OpMath.2013.33.4.741

Opuscula Mathematica

# Vulnerability parameters of tensor product of complete equipartite graphs

P. Paulraja
V. Sheeba Agnes

Abstract. 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.

Keywords: fault tolerance, tensor product, vulnerability parameters.

Mathematics Subject Classification: 05C76, 05C40.

Full text (pdf)

P. Paulraja, V. Sheeba Agnes, Vulnerability parameters of tensor product of complete equipartite graphs, Opuscula Math. 33, no. 4 (2013), 741-750, http://dx.doi.org/10.7494/OpMath.2013.33.4.741

a .bib file (BibTeX),
a .ris file (RefMan),
a .enw file (EndNote)
or export to RefWorks.

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.