Extremality of graph entropy based on degrees of uniform hypergraphs with few edges

2017/09/27 by Hu, Dan, Li, Xueliang, Liu, Xiaogang +1
#05C50 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1709.09594

Abstract

Let H be a hypergraph with n vertices. Suppose that d₁,d₂,…,d_n are degrees of the vertices of H. The t-th graph entropy based on degrees of H is defined as I_d^t(H) =-∑_i=1ⁿ(\fracd_i^t∑_j=1ⁿd_j^tlog\fracd_i^t∑_j=1ⁿd_j^t) =log(∑_i=1ⁿd_i^t)-∑_i=1ⁿ(\fracd_i^t∑_j=1ⁿd_j^tlog d_i^t), where t is a real number and the logarithm is taken to the base two. In this paper we obtain upper and lower bounds of I_d^t(H) for t=1, when H is among all uniform supertrees, unicyclic uniform hypergraphs and bicyclic uniform hypergraphs, respectively.

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