##### 1. A GRAPH WHICH RECOGNIZES IDEMPOTENTS OF A COMMUTATIVE RING

H. Dorbidi; S. Alikhani

Volume 7, Issue 2 , Winter and Spring 2020, , Pages 143-154

##### Abstract
In this paper we introduce and study a graph on the set of ideals of a commutative ring $R$. The vertices of this graph are non-trivial ideals of $R$ and two distinct ideals $I$ and $J$ are adjacent if and only $IJ=I\cap J$. We obtain some properties of this graph and study its relation to the structure ...  Read More

##### 2. TOTAL DOMINATION POLYNOMIAL OF GRAPHS FROM PRIMARY SUBGRAPHS

S. Alikhani; N. Jafari

Volume 5, Issue 2 , Winter and Spring 2018, , Pages 127-138

##### Abstract
Let $G = (V, E)$ be a simple graph of order $n$. The total dominating set is a subset $D$ of $V$ that every vertex of $V$ is adjacent to some vertices of $D$. The total domination number of $G$ is equal to minimum cardinality of total dominating set in $G$ and denoted by $\gamma_t(G)$. The total domination ...  Read More

##### 3. ON THE EDGE COVER POLYNOMIAL OF CERTAIN GRAPHS

S. Alikhani; S. Jahari

Volume 2, Issue 2 , Winter and Spring 2015, , Pages 97-108

##### Abstract
Let $G$ be a simple graph of order $n$ and size $m$. The edge covering of $G$ is a set of edges such that every vertex of $G$ is incident to at least one edge of the set. The edge cover polynomial of $G$ is the polynomial$E(G,x)=sum_{i=rho(G)}^{m} e(G,i) x^{i}$, where $e(G,i)$ is the number of edge coverings ...  Read More