arXiv subjects

Fatemeh Aghaei

Publications and source records attributed to Fatemeh Aghaei.

6 recordsLinked to original sources

arXiv2026

Superstable Geometry in Triadic Percolation

Triadic percolation turns bond percolation into a dynamical problem governed by an effective one-dimensional unimodal map. We show that the geometry of superstable cycles provides a direct, map-agnostic probe of local nonlinearity: specifically, the distance from the map's maximum to a distinguished next-to-maximum point on the attracting $2^n$-cycle (which coincides with a preimage of the maximum at $2^n$-superstability) scales as $|Δp|^γ$ with $γ= 1/z$, where $z$ is the nonflat order of the maximum. This prediction is verified across canonical unimodal families and heterogeneous triadic ensembles, with Lyapunov spectra corroborating the one-dimensional reduction. A derivative condition on the activation kernel fixes the local nonlinearity order $z$ (and thus, under standard unimodal-map hypotheses, the associated $z$-logistic universality class) and gives conditions under which $z>2$ can be realized. The diagnostic operates directly on orbit data under standard regularity assumptions, providing a practical tool to classify universality in higher-order networks.

cond-mat.stat-mech↗

arXiv2025

$2$-Restricted Optimal Pebbling Number of Some Graphs

Let $G=(V,E)$ be a simple graph. A pebbling configuration on $G$ is a function $f:V\rightarrow \mathbb{N}\cup \{0\}$ that assigns a non-negative integer number of pebbles to each vertex. The weight of a configuration $f$ is $w(f)=\sum_{u\in V}f(u)$, the total number of pebbles. A pebbling move consists of removing two pebbles from a vertex $u$ and placing one pebble on an adjacent vertex $v$. A configuration $f$ is a $t$-restricted pebbling configuration ($t$RPC) if no vertex has more than $t$ pebbles. The $t$-restricted optimal pebbling number $π_t^*(G)$ is the minimum weight of a $t$RPC on $G$ that allows any vertex to be reached by a sequence of pebbling moves. The distinguishing number $D(G)$ is the minimum number of colors needed to label the vertices of $G$ such that the only automorphism preserving the coloring is the trivial one (i.e., the identity map). In this paper, we investigate the $2$-restricted optimal pebbling number of trees $T$ with $D(T)=2$ and radius at most $2$ and enumerate their $2$-restricted optimal pebbling configurations. Also we study the $2$-restricted optimal pebbling number of some graphs that are of importance in chemistry such as some alkanes.

math.CO↗

arXiv2024

Domination polynomial and total domination polynomial of zero-divisor graphs of commutative rings

The domination polynomial (the total domination polynomial) of a graph $ G $ of order $ n $ is the generating function of the number of dominating sets (total dominating sets) of $ G $ of any size. In this paper, we study the domination polynomial and the total domination polynomial of zero-divisor graphs of the ring $ \mathbb{Z}_n $ where $ n\in\lbrace 2p, p^2, pq, p^2q, pqr, p^α\rbrace $, and $ p, q, r $ are primes with $ p>q>r>2 $.

math.CO↗

arXiv2024

Pebbling number of polymers

Let $G=(V,E)$ be a simple graph. A function $f:V\rightarrow \mathbb{N}\cup \{0\}$ is called a configuration of pebbles on the vertices of $G$ and the quantity $\vert f\vert=\sum_{u\in V}f(u)$ is called the weight of $f$ which is just the total number of pebbles assigned to vertices. A pebbling step from a vertex $u$ to one of its neighbors $v$ reduces $f(u)$ by two and increases $f(v)$ by one. A pebbling configuration $f$ is said to be solvable if for every vertex $ v $, there exists a sequence (possibly empty) of pebbling moves that results in a pebble on $v$. The pebbling number $ π(G) $ equals the minimum number $ k $ such that every pebbling configuration $ f $ with $ \vert f\vert = k $ is solvable. Let $ G $ be a connected graph constructed from pairwise disjoint connected graphs $ G_1,...,G_k $ by selecting a vertex of $ G_1 $, a vertex of $ G_2 $, and identifying these two vertices. Then continue in this manner inductively. We say that $ G $ is a polymer graph, obtained by point-attaching from monomer units $ G_1,...,G_k $. In this paper, we study the pebbling number of some polymers.

math.CO↗

arXiv2024

More on graph pebbling number

Let $G=(V,E)$ be a simple graph. A function $ϕ:V\rightarrow \mathbb{N}\cup \{0\}$ is called a configuration of pebbles on the vertices of $G$ and the quantity $\sum_{u\in V}ϕ(u)$ is called the size of $ϕ$ which is just the total number of pebbles assigned to vertices. A pebbling step from a vertex $u$ to one of its neighbors $v$ reduces $ϕ(u)$ by two and increases $ϕ(v)$ by one. Given a specified target vertex $r$ we say that $ϕ$ is $t$-fold $r$-solvable, if some sequence of pebbling steps places at least $t$ pebbles on $r$. Conversely, if no such steps exist, then $ϕ$ is $r$-unsolvable. The minimum positive integer $m$ such that every configuration of size $m$ on the vertices of $G$ is $t$-fold $r$-solvable is denoted by $π_t(G,r)$. The $t$-fold pebbling number of $G$ is defined to be $π_t(G)= max_{r\in V(G)}π_t(G,r)$. When $t=1$, we simply write $π(G)$, which is the pebbling number of $G$. In this note, we study the pebbling number for some specific graphs. Also we investigate the pebbling number of corona and neighbourhood corona of two graphs.

math.CO↗

arXiv2023

More on the $2$-restricted optimal pebbling number

Let $G=(V,E)$ be a simple graph. A function $f:V\rightarrow \mathbb{N}\cup \{0\}$ is called a configuration of pebbles on the vertices of $G$ and the weight of $f$ is $w(f)=\sum_{u\in V}f(u)$ which is just the total number of pebbles assigned to vertices. A pebbling step from a vertex $u$ to one of its neighbors $v$ reduces $f(u)$ by two and increases $f(v)$ by one. A pebbling configuration $f$ is said to be solvable if for every vertex $ v $, there exists a sequence (possibly empty) of pebbling moves that results in a pebble on $v$. A pebbling configuration $f$ is a $t$-restricted pebbling configuration (abbreviated $t$RPC) if $f(v)\leq t$ for all $v\in V$. The $t$-restricted optimal pebbling number $π_t^*(G)$ is the minimum weight of a solvable $t$RPC on $G$. Chellali et.al. [Discrete Appl. Math. 221 (2017) 46-53] characterized connected graphs $G$ having small $2$-restricted optimal pebbling numbers and characterization of graphs $G$ with $π_2^*(G)=5$ stated as an open problem. In this paper, we solve this problem. We improve the upper bound of the $2$-restricted optimal pebbling number of trees of order $n$. Also, we study $2$-restricted optimal pebbling number of some grid graphs, corona and neighborhood corona of two specific graphs.

math.CO↗