arXiv subjects

S. Alikhani

Publications and source records attributed to S. Alikhani.

4 recordsLinked to original sources

arXiv2025

Independent domination bondage number in graphs

A non-empty set $S\subseteq V (G)$ of the simple graph $G=(V(G),E(G))$ is an independent dominating set of $G$ if every vertex not in $S$ is adjacent with some vertex in $S$ and the vertices of $S$ are pairwise non-adjacent. The independent domination number of $G$, denoted by $\gamma_i(G)$, is the minimum size of all independent dominating sets of $G$. The independent domination bondage number of $G$ is the minimum number of edges whose removal changes the independent domination number of $G$. In this paper, we investigate properties of independent domination bondage number in graphs. In particular, we obtain several bounds and obtain the independent domination bondage number of some operations of two graphs.

math.CO↗

arXiv2020

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

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 (recursively) $k$-times of the MZ-method for the number $x$, produces a graph with unique structure that is denoted by $G_k(x)$. We investigate the structure of $G_k(x)$. Also from the natural number $x$ and graph $G_k(x)$ we produce codes which are important and applicable in the information security and cryptography.

cs.DM↗

arXiv2015

Some families of graphs with no nonzero real domination roots

Let G be a simple graph of order n. The domination polynomial is the generating polynomial for the number of dominating sets of G of each cardinality. A root of this polynomial is called a domination root of G. Obviously 0 is a domination root of every graph G. In the study of the domination roots of graphs, this naturally raises the question: which graphs have no nonzero real domination roots? In this paper we present some families of graphs whose have this property.

math.CO↗

arXiv2014

Domination polynomials of k-tree related graphs

Let $G$ be a simple graph of order $n$. The domination polynomial of $G$ is the polynomial $D(G, x)=\sum_{i=γ(G)}^{n} d(G,i) x^{i}$, where $d(G,i)$ is the number of dominating sets of $G$ of size $i$ and $γ(G)$ is the domination number of $G$. In this paper we study the domination polynomials of several classes of $k$-tree related graphs. Also, we present families of these kind of graphs, whose domination polynomial have no nonzero real roots.

math.CO↗