arXiv subjects
Publications and source records attributed to Bijo S Anand.
This article discusses $Δ$-convexity on simple connected graphs. We establish general bounds for the Helly number, Radon number, and rank with respect to $Δ$-convexity on graphs. Additionally, we give the exact values for the Helly number and Radon number for chordal graphs, as well as the rank for block graphs.
Let $D=(V,E)$ be a strongly connected digraph and let $u ,v\in V(D)$. The maximum distance $md (u,v)$ is defined as\\ $md(u,v)$=max\{$\overrightarrow{d}(u,v), \overrightarrow{d}(v,u)$\} where $\overrightarrow{d}(u,v)$ denote the length of a shortest directed $u-v$ path in $D$. This is a metric. The boundary, contour, eccentric and peripheral sets of a strong digraph $D$ with respect to this metric have been defined, and the above said metrically defined sets of a large strong digraph $D$ have been investigated in terms of the factors in its prime factor decomposition with respect to Cartesian product. In this paper we investigate about the above boundary-type sets of a strong digraph $D$ in terms of the factors in its prime factor decomposition with respect to strong product.