Abstract
For a graph G with degree sequence (d1,d2,…,dn) and a positive integer p, denote the degree power of G by ep(G)=∑i=1ndip. In this paper, we concentrate on the extremal problems of degree powers in graphs with fixed size. By the majorization theory, we firstly characterize the graphs with the maximum ep(G) among all connected graphs in G(n,m) where m≤2n−3. The second main result is about the graphs with forbidden cycles. Concretely, we determine the maximum ep(G) among all Cℓ-free graphs in G(m) and characterize the corresponding extremal graphs. An analogous result is obtained in non-bipartite graphs. Furthermore, we respectively give the sharp upper bounds on ep(G) in G(m) with respect to various graph parameters, such as clique number, chromatic number, girth, and circumference.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
