8 research outputs found
Proximity, remoteness and maximum degree in graphs
The average distance of a vertex of a connected graph is the
arithmetic mean of the distances from to all other vertices of . The
proximity and the remoteness of are the minimum and the
maximum of the average distances of the vertices of , respectively.
In this paper, we give upper bounds on the remoteness and proximity for
graphs of given order, minimum degree and maximum degree. Our bounds are sharp
apart from an additive constant.Comment: 20 page
Proximity and Remoteness in Graphs: a survey
The proximity of a connected graph is the minimum, over
all vertices, of the average distance from a vertex to all others. Similarly,
the maximum is called the remoteness and denoted by . The
concepts of proximity and remoteness, first defined in 2006, attracted the
attention of several researchers in Graph Theory. Their investigation led to a
considerable number of publications. In this paper, we present a survey of the
research work.Comment: arXiv admin note: substantial text overlap with arXiv:1204.1184 by
other author