On Dinstances in Some Bipartite Graphs
Publications de l'Institut Mathématique, (N.S.) 43 (1988) no. 57.

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Let $d(v|G)$ 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 $d(v|G)\equiv 1\pmod k$ 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, $W(G)\equiv W(H)\pmod{2k^2}$. 
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     author = {Ivan Gutman},
     title = {On {Dinstances} in {Some} {Bipartite} {Graphs}},
     journal = {Publications de l'Institut Math\'ematique},
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     publisher = {mathdoc},
     volume = {(N.S.) 43},
     number = {57},
     year = {1988},
     url = {https://geodesic-test.mathdoc.fr/item/PIM_1988_N_S_43_57_a0/}
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Ivan Gutman. On Dinstances in Some Bipartite Graphs. Publications de l'Institut Mathématique, (N.S.) 43 (1988) no. 57. https://geodesic-test.mathdoc.fr/item/PIM_1988_N_S_43_57_a0/