PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 43(57), pp. 38 (1988) 

On dinstances in some bipartite graphsIvan GutmanPrirodnomatematicki fakultet, Kragujevac, YugoslaviaAbstract: Let $d(vG)$ be the sum of the dinstances between a vertex $v$ of a graph $G$ and all other vertices of $G$. Let $W (G)$ be the sum of the distances between all pairs of vertices of $G$. A class {\bf C}$(k)$ of bipartite graphs is found, such that $d(vG)\equiv 1\pmod k$ holds for an arbitrary vertex of an arbitrary member of {\bf C}$(k)$. Further, for two members $G$ and $H$ of {\bf C}$(k)$, having equal cyclomatic number, $W(G)\equiv W(H)\pmod{2k^2}$. Classification (MSC2000): 03C50 Full text of the article:
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© 2001 Mathematical Institute of the Serbian Academy of Science and Arts
