TY - JOUR
ID - 3024
TI - A note on the extended total graph of commutative rings
JO - Journal of Algebra and Related Topics
JA - JART
LA - en
SN - 2345-3931
AU - Esmaeili Khalil Saraei, F.
AU - Navidinia, E.
AD - University of Tehran
AD - Department of Mathematics, University of Guilan, Rasht, Iran
Y1 - 2018
PY - 2018
VL - 6
IS - 1
SP - 25
EP - 33
KW - Total graph
KW - prime ideal
KW - multiplicative-prime subset
DO - 10.22124/jart.2018.10241.1101
N2 - 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 $p,qin R$, the vertices $p$ and $q$ are adjacent if and only if $rp+sqin H$ for some $r,sin Rsetminus H$. We also study the two (induced) subgraphs $ET_{H}(H)$ and $ET_{H}(Rsetminus H)$, with vertices $H$ and $Rsetminus H$, respectively. Among other things, the diameter and the girth of $ET_{H}(R)$ are also studied.
UR - https://jart.guilan.ac.ir/article_3024.html
L1 - https://jart.guilan.ac.ir/article_3024_c7a72ce759419a2bcd9ddd57dcf4da67.pdf
ER -