Abstract The amount of Internet data is increasing day by with the rapid development information technology. To process massive amounts and solve overload, researchers proposed recommender systems. Traditional recommendation methods are mainly based on collaborative filtering algorithms, which have sparsity problems. At present, most model-based algorithms can only capture first-order semantic ...

Let G=(V,E) be a simple connected graph of order p and size q. A decomposition of a graph G is a collection π of edge-disjoint subgraphs G_1,G_2,…,G_n of G such that every edge of G belongs to exactly one G_i,(1≤i ≤n). The decomposition 〖π={G〗_1,G_2,…,G_n} of a connected graph G is said to be a distinct edge geodetic decomposition if g_1 (G_i )≠g_1 (G_j ),(1≤i≠j≤n). The maximum cardinality of π...

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 of $g$ of size $i$, and$rho(g)$ is the edge covering number of $g$. in this paper we stud...

This paper focuses on the average order of dominating sets a graph. We find extremal graphs for maximum and minimum value over all n vertices, while trees we prove that star minimizes sets. in without isolated vertices is at most 3n/4, but provide evidence actual upper bound 2n/3. Finally, show normalized average, dense [1/2,1], tends to 12 almost graphs.

let $g$ be a simple graph of order $n$‎. ‎we consider the‎ ‎independence polynomial and the domination polynomial of a graph‎ ‎$g$‎. ‎the value of a graph polynomial at a specific point can give‎ ‎sometimes a very surprising information about the structure of the‎ ‎graph‎. ‎in this paper we investigate independence and domination‎ ‎polynomial at $-1$ and $1$‎.