English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we investigate the energy of a weighted random graph $G_p(f)$in $G_{n,p}(f)$, in which each edge $ij$ takes the weight $f(d_i,d_j)$, where$d_v$ is a random variable, the degree of vertex $v$ in the random graph $G_p$of the Erd\"{o}s--R\'{e}nyi random graph model $G_{n,p}$, and $f$ is asymmetric real function on two variables. Suppose $|f(d_i,d_j)|\leq C n^m$ forsome constants $C, m>0$, and $f((1+o(1))np,(1+o(1))np)=(1+o(1))f(np,np)$. Then,for almost all graphs $G_p(f)$ in $G_{n,p}(f)$, the energy of $G_p(f)$ is$(1+o(1))f(np,np)\frac{8}{3\pi}\sqrt{p(1-p)}\cdot n^{3/2},$ where $p\in(0,1)$is any fixed and independent of $n$. Consequently, with this one basket we canget the asymptotic values of various kinds of graph energies of chemical use,such as Randi\'c energy, ABC energy, and energies of random matrices obtainedfrom various kinds of degree-based chemical indices.

The asymptotic value of graph energy for random graphs with degree-based weights