University of Guilan Journal of Algebra and Related Topics 2345-3931 13 1 2025 07 01 A note on total graph of commutative krasner hyperrings 87 97 8440 10.22124/jart.2024.24911.1553 EN E. Navidinia ‎Department of Mathematics, University of Mohaghegh Ardabili, Ardabil, Iran A. Khojali Department of Mathematics, University of Mohaghegh Ardabili, Ardabil, Iran F. Esmaeili Khalil Saraei Fouman Faculty of Engineering, College of Engineering, University of Tehran, Fouman, Iran Journal Article 2023 07 12 The purpose of this paper is to introduce the notion of total graph of Krasner hyperrings. In this regard, a connection between the graph theory and the theory of hyperrings is constructed and some fundamental properties of the total graph of Krasner hyperrings are investigated. Finally, for a multiplicative-prime subset $H$ of a hyperring $R$, the diameter and the girth of $\Gamma_{\!\!H}(R\setminus H)\,\mbox{and}\, \Gamma_{\!\!H}(H)$ are computed precisely. https://jart.guilan.ac.ir/article_8440_c61114a62165a04f2aab15fbfafc8c99.pdf