On Dinstances in Some Bipartite Graphs

Ivan Gutman

Geodesic

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On Dinstances in Some Bipartite Graphs

Ivan Gutman

Publications de l'Institut Mathématique, _N_S_43 (1988) no. 57, p. 3 .

Voir la notice de l'article dans eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Résumé

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 (\mod 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) (\mod 2 k^{2})

Classification : 03C50

@article{PIM_1988_N_S_43_57_a0,
     author = {Ivan Gutman},
     title = {On {Dinstances} in {Some} {Bipartite} {Graphs}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {3 },
     publisher = {mathdoc},
     volume = {_N_S_43},
     number = {57},
     year = {1988},
     language = {en},
     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, p. 3 . https://geodesic-test.mathdoc.fr/item/PIM_1988_N_S_43_57_a0/