Radius, diameter and the degree sequence of a graph

Rok, strany: 2015, 1223 - 1236

We give asymptotically sharp upper bounds on the radius and diameter of (i) a connected graph, (ii) a connected triangle-free graph, (iii) a connected $C₄$-free graph of given order, minimum degree, and maximum degree. We also give better bounds on the radius and diameter for triangle-free graphs with a given order, minimum degree and a given number of distinct terms in the degree sequence of the graph. Our results improve on old classical theorems by Erdős, Pach, Pollack and Tuza [Radius, diameter, and minimum degree, J. Combin. Theory Ser. B 47 (1989), 73--79] on radius, diameter and minimum degree.

ISO 690:

Mazorodze, J., Mukwembi, S. 2015. Radius, diameter and the degree sequence of a graph. In Mathematica Slovaca, vol. 65, no.6, pp. 1223-1236. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0084

APA:

Mazorodze, J., Mukwembi, S. (2015). Radius, diameter and the degree sequence of a graph. Mathematica Slovaca, 65(6), 1223-1236. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0084