Bounds on the Spanner-Sum of Torus
Bommanahal Basavanagoud, Jaishri B. Veeragoudar · Journal of Discrete Mathematical Sciences and Cryptography · 2015
For a spanning tree T of G, the spanner-sum is defined by ζ s (T, G) = ∑dT (u, v) where (u, v) ∈ E(G) \ E(T) and dT (u, v) denotes the distance between u and v in T. Then, the minimum spanner-sum of G is defined as ζ s (G) = minζ s (T, G) where the minimum is taken over all spanning trees T of G. The spanner-sum problem of a graph G is to find a spanning tree T of G that induces the minimum spanner-sum ζ s (G). In this paper, we estimate bounds for the spanner-sum of torus.