@article {
author = {Esmaeili Khalil Saraei, F. and Navidinia, E.},
title = {A note on the extended total graph of commutative rings},
journal = {Journal of Algebra and Related Topics},
volume = {6},
number = {1},
pages = {25-33},
year = {2018},
publisher = {University of Guilan},
issn = {2345-3931},
eissn = {2382-9877},
doi = {10.22124/jart.2018.10241.1101},
abstract = {Let $R$ be a commutative ring and $H$ a nonempty proper subset of $R$.In this paper, the extended total graph, denoted by $ET_{H}(R)$ is presented, where $H$ is amultiplicative-prime subset of $R$. It is the graph with all elements of $R$ as vertices, and for distinct $p,q\in R$, the vertices $p$ and $q$ are adjacent if and only if $rp+sq\in H$ for some $r,s\in R\setminus H$. We also study the two (induced) subgraphs $ET_{H}(H)$ and $ET_{H}(R\setminus H)$, with vertices $H$ and $R\setminus H$, respectively. Among other things, the diameter and the girth of $ET_{H}(R)$ are also studied.},
keywords = {Total graph,prime ideal,multiplicative-prime subset},
url = {https://jart.guilan.ac.ir/article_3024.html},
eprint = {https://jart.guilan.ac.ir/article_3024_c7a72ce759419a2bcd9ddd57dcf4da67.pdf}
}