The connection between line-connectivity concepts of graphs and indices of network reliability is well-known. Of particular interest in such studies are the circulant graphs because the connected ones have the largest possible value of line-connectivity λ of p-point, degree r, regular graphs, namely λ = r. In this work, we define the higher order line-connectivity measure Nᵢ as the number of line-disconnecting sets of order i. Regular degree r, p-point graphs having λ = r satisfy N_λ p. Such graphs which attain this lower bound are called super-λ. In this work we determine the necessary and sufficient conditions for a circulant to be super-λ. In addition we determine a lower bound on Nᵢ for λ i 2r - 3. It is shown that a special class of circulants, known as Harary graphs, achieve this lower bound for all these values of i.
No takes yet. Share an insight, caveat, or question.
Boesch et al. (1986) studied this question.
Synapse has enriched 3 closely related papers on similar clinical questions. Consider them for comparative context: