Distance strings of the vertices of certain graphs

Abstract

The notion of the distance string of a vertex $v_i \in V(G)$ which is denoted by, $\tau(v_i)$ is introduced. Distance strings permit a new approach to determining the induced vertex stress, the total induced vertex stress and total vertex stress (sum of vertex stress over all vertices) of a graph. A seemingly under-studied topic i.e. the eccentricity of a vertex of a bipartite Kneser graph $BK(n,k)$, $n \geq 2k + 1$ has been furthered. A surprisingly simple result was established, namely for $k \geq 2$, $diam(BK(n,k)) = 5$ if $n = 2k + 1$ and $diam(BK(n,k)) = 3$ if $n \neq 2k + 1$.