@article {
author = {Samaie, Sara and Iranmanesh, Ali and Tehranian, Abolfazl and Hosseinzadeh, Mohammad Ali},
title = {Expected Value of Zagreb Indices of Random Bipartite Graphs},
journal = {Iranian Journal of Mathematical Chemistry},
volume = {15},
number = {1},
pages = {27-37},
year = {2024},
publisher = {University of Kashan},
issn = {2228-6489},
eissn = {2008-9015},
doi = {10.22052/ijmc.2023.253969.1794},
abstract = {In this paper, we calculate the expected values of the first and second Zagreb indices, denoted as $\textbf{E}\left(M_1\right)$ and $\textbf{E}\left(M_2\right)$ respectively, as well as the expected value of the forgotten index, $\textbf{E}\left(F\right)$, for two models of random bipartite graphs. To evaluate our findings, we establish the growth rate by demonstrating that for a random bipartite graph $G$ of order $n$ in either model, the expected value of $M_1(G)$ is $O\left( n^3 \right)$. Furthermore, we prove that the expected values of $M_2(G)$ and $F(G)$ are both $O\left( n^4 \right)$.},
keywords = {Random bipartite graphs,Random symmetric $(0,1)$-matrix,Zagreb indices,Expected value},
url = {https://ijmc.kashanu.ac.ir/article_114247.html},
eprint = {https://ijmc.kashanu.ac.ir/article_114247_d931f5df92563abca438a67a5c0870e6.pdf}
}