Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Graphs with minimum degree-based entropy   The degree-based entropy of a graph is defined as the Shannon entropy based
on the information functional that associates the vertices of the graph with
the corresponding degrees. In this paper, we study extremal problems of finding
the graphs attaining the minimum degree-based graph entropy among graphs and
bipartite graphs with a given number of vertices and edges. We characterize the
unique extremal graph achieving the minimum value among graphs with a given
number of vertices and edges and present a lower bound for the degree-based
entropy of bipartite graphs and characterize all the extremal graphs which
achieve the lower bound. This implies the known result due to Cao et al. (2014)
that the star attains the minimum value of the degree-based entropy among trees
with a given number of vertices.

31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio