TY - JOUR
T1 - On Wiener and multiplicative Wiener indices of graphs
AU - Das, Kinkar Ch
AU - Gutman, Ivan
N1 - Publisher Copyright:
© 2016 Elsevier B.V.
PY - 2016/6/19
Y1 - 2016/6/19
N2 - Let G be a connected graph of order n with m edges and diameter d. The Wiener index W(G) and the multiplicative Wiener index π(G) of the graph G are equal, respectively, to the sum and product of the distances between all pairs of vertices of G. We obtain a lower bound for the difference π(G)-W(G) of bipartite graphs. From it, we prove that π(G)>W(G) holds for all connected bipartite graphs, except P2, P3, and C4. We also establish sufficient conditions for the validity of π(G)>W(G) in the general case. Finally, a relation between W(G), π(G), n, m, and d is obtained.
AB - Let G be a connected graph of order n with m edges and diameter d. The Wiener index W(G) and the multiplicative Wiener index π(G) of the graph G are equal, respectively, to the sum and product of the distances between all pairs of vertices of G. We obtain a lower bound for the difference π(G)-W(G) of bipartite graphs. From it, we prove that π(G)>W(G) holds for all connected bipartite graphs, except P2, P3, and C4. We also establish sufficient conditions for the validity of π(G)>W(G) in the general case. Finally, a relation between W(G), π(G), n, m, and d is obtained.
KW - Diameter (of graph)
KW - Distance (in graph)
KW - Multiplicative Wiener index
KW - Wiener index
UR - https://www.scopus.com/pages/publications/84976217069
U2 - 10.1016/j.dam.2016.01.037
DO - 10.1016/j.dam.2016.01.037
M3 - Article
AN - SCOPUS:84976217069
SN - 0166-218X
VL - 206
SP - 9
EP - 14
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
ER -