International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 21, Pages 3419-3426

A class of inequalities relating degrees of adjacent nodes to the average degree in edge-weighted uniform hypergraphs

P. D. Johnson Jr.1 and R. N. Mohapatra2

1Department of Mathematics and Statistics, College of Science and Mathematics, Auburn University, 36849-5307, AL, USA
2Department of Mathematics, College of Arts and Sciences, University of Central Florida, Orlando 32816-1364, FL, USA

Received 26 August 2004; Revised 28 September 2005

Copyright © 2005 P. D. Johnson and R. N. Mohapatra. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In 1986, Johnson and Perry proved a class of inequalities for uniform hypergraphs which included the following: for any such hypergraph, the geometric mean over the hyperedges of the geometric means of the degrees of the nodes on the hyperedge is no less than the average degree in the hypergraph, with equality only if the hypergraph is regular. Here, we prove a wider class of inequalities in a wider context, that of edge-weighted uniform hypergraphs.