Saeid Alikhani

activity

20192026

collaborators

8 papers

math.CO2026

On the Integer Domination Root Conjecture

Saeid Alikhani, Max Griswold

The domination integer root conjecture asserted that $0$ and $- 2$ are the only integer roots of the domination polynomial $D (G, x)$ for any graph $G$ . In this paper, we document a…

math.CO2026

On the Spectrum of the Line Graph of a Family of Bipartite Graphs Arising from the Boolean Lattice

Ali Zafari, Saeid Alikhani

The Boolean lattice $B L_{n}$ , $n \geq 3$ , is the graph whose vertex set is the collection of all subsets of $[n] = {1, 2, \dots, n}$ , where two subsets $U$ and $W$ are adjacent if and o…

math.CO2026

On the Number of Connected Edge Cover Sets of Some Graph Families

Ali Zeydi Abdian, Saeid Alikhani, Mahsa Zare

Let $G = (V, E)$ be a simple connected graph. A connected edge cover of $G$ is a subset $S \subseteq E$ such that every vertex of $G$ is incident with at least one edge in $S$ and the…

math.HO2025

Amicable numbers and their connection to the Euler totient function

Ali Reza Mavaddat, Saeid Alikhani

A pair of numbers is amicable if each number equals the sum of the proper divisors of the other. This paper after exploring the history and evolution of amicable numbers, introduce…

math.CO2025

Some results on Hamming graphs and an extended Hamming graphs

Ali Zafari, Saeid Alikhani

In this paper we first obtain the spectrum of the folded hypercube in a new approach. Then we introduce a new family of graphs called the extended Hamming graph, denoted by $EH(n,2…

math.CO2025

On the Harmonic characteristic polynomial of specific graphs

Sadruddin Rahimi, Saeid Alikhani

This paper explores the Harmonic matrix $M H (G)$ associated with a simple graph $G$ , where each entry corresponds to $\frac{2}{d _{i} + d _{j}}$ for adjacent vertices $v_{i}$ and $ v_…

cs.DM2020

Graphs and codes produced by a new method for dividing a natural number by two

M. Zeynali Azim, M. A. Jabraeil Jamali, B. Anari +2

In this paper, we introduce a new method which we call it MZ-method, for dividing a natural number $x$ by two and then we use graph as a model to show MZ-algorithm. Applying (recur…

math.CO2019

On the spectrum of two families of non-distance-regular graphs

Ali Zafari, Saeid Alikhani

This paper addresses the challenge of spectral analysis and structural investigation for graphs that are not distance-regular, where computing the spectrum using standard methods b…