7 papers
On the Integer Domination Root Conjecture
Saeid Alikhani, Max Griswold
The domination integer root conjecture asserted that and are the only integer roots of the domination polynomial for any graph . In this paper, we document a…
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 , , is the graph whose vertex set is the collection of all subsets of , where two subsets and are adjacent if and o…
On the Number of Connected Edge Cover Sets of Some Graph Families
Ali Zeydi Abdian, Saeid Alikhani, Mahsa Zare
Let be a simple connected graph. A connected edge cover of is a subset such that every vertex of is incident with at least one edge in and the…
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…
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…
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…