Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
419330 | Discrete Applied Mathematics | 2014 | 9 Pages |
Abstract
The remoteness ρ=ρ(G)ρ=ρ(G) of a connected graph GG is the maximum, over all vertices, of the average distance from a vertex to all others, while the proximity π=π(G)π=π(G) of a connected graph GG is the minimum, over all vertices, of the average distance from a vertex to all others. In this paper, we first deal with some conjectures on remoteness and proximity, among which two conjectures were proved, while the other two conjectures were disproved by counter examples. Then we obtain some new upper bounds for remoteness and proximity in terms of some graph invariants. Moreover, we use remoteness to give a new sufficient condition for a connected bipartite graph to be Hamiltonian.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Hongbo Hua, Kinkar Ch. Das,