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Mahdi Anbarloei

Publications and source records attributed to Mahdi Anbarloei.

27 records · Page 2Linked to original sources
arXiv2022

Some hyperideals defined on the basis of the intersection of all n-ary prime hyperideals

Various classes of hyperideals have been studied in many papers in order to let us fully understand the structures of hyperrings in general. The purpose of this paper is the study of some hyperideals whose concept is created on the basis of the intersection of all n-ary prime hyperideals in category of Krasner (m,n)-hyperrings. In this regard we introduce notions of N-hyperideals, delta-N-hyperideals, (k,n)-absorbing delta-N-hyperideals and S-N-hyperideals. The overall framework of these structures in then explaind, providing a number of major conclusions.

math.AC↗
arXiv2021

A note on two classes of hyperideals

In this paper, we define the concepts of r-hyperideal and n-hyperideal of the multiplicative hyperring R which are two new classes of hyperideals. Several properties of them are provided.

math.AC↗
arXiv2021

2-Prime Hyperideals

Multiplicative hyperrings are an important class of algebraic hyperstructures which generalize rings further to allow multiple output values for the multiplication operation. Let R be a commutative multiplicative hyperring. The 2-prime hyperideals are a generalization of prime hyperideals. In this paper, we aim to study 2-prime hyperideals and give some results. Moreover, we investigate delta-2-primary hyperideals which are an expansion of 2-prime hyperideals.

math.AC↗
arXiv2021

On 1-absorbing prime hyperideal and some of its generalizations

Let R be a multiplicative hyperring. In this paper, we define the concept of 1-absorbing prime hyperideals which is a generalization of the prime hyperideals. Several properties of the hyperideals are provided. Moreover, we introduce the notions of 1-absorbing primary hyperideals, strongly 1-absorbing primary hyperideals and weakly 1-absorbing primary hyperideals which are generalizations of the 1-absorbing prime hyperideals and then we will show some properties of them.

math.AC↗
arXiv2014

On the Randic and degree distance indices of the Mycielskian of a graph

In a search for triangle-free graphs with arbitrarily large chromatic numbers, Mycielski developed a graph transformation that transforms a graph into a new graph which is called the Mycielskian of that graph. In this paper we provide some sharp bounds for the Randic index of the Mycielskian graphs. Also, we determine the degree distance index of the Mycielskian of each graph with diameter two.

math.CO↗
arXiv2013

A Bound for the Locating Chromatic Numbers of Trees

Let $f$ be a proper $k$-coloring of a connected graph $G$ and $Π=(V_1,V_2,\ldots,V_k)$ be an ordered partition of $V(G)$ into the resulting color classes. For a vertex $v$ of $G$, the color code of $v$ with respect to $Π$ is defined to be the ordered $k$-tuple $c_{{}_Π}(v)=(d(v,V_1),d(v,V_2),\ldots,d(v,V_k)),$ where $d(v,V_i)=\min\{d(v,x): x\in V_i\}, 1\leq i\leq k$. If distinct vertices have distinct color codes, then $f$ is called a locating coloring. The minimum number of colors needed in a locating coloring of $G$ is the locating chromatic number of $G$, denoted by $\Cchi_{{}_L}(G)$. In this paper, we study the locating chromatic numbers of trees. We provide a counter example to a theorem of Gary Chartrand et al. [G. Chartrand, D. Erwin, M.A. Henning, P.J. Slater, P. Zhang, The locating-chromatic number of a graph, Bull. Inst. Combin. Appl. 36 (2002) 89-101] about the locating chromatic numbers of trees. Also, we offer a new bound for the locating chromatic number of trees. Then, by constructing a special family of trees, we show that this bound is best possible.

math.CO↗