Dounia Lotfi

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The number of spanning trees of a map C denoted by τ(C) is the total number of distinct spanning subgraphs of C that are trees. A maximal planar map is a simple graph G formed by n vertices, 3(n − 2) edges and all faces having degree 3 [2]. In this paper, we derive the explicit formula for the number of spanning trees of the maximal planar map and deduce a(More)
The number of spanning trees of a map C is the total number of distinct spanning subgraphs of C that are trees. In this paper, we give some methods to facilitate the calculation of the number of spanning trees for planar maps and derive several simple formulas for the number of spanning trees of special families of maps called (n-Tent chains, n-Home chains,(More)
In this paper, we investigate the number of spanning trees in planar graphs with two cut vertices. We propose a combinatorial approach based on the contraction method, in order to derive spanning trees recursions for this class of graphs. Applications on different graphs showed the efficiency and the simplicity of our recursive approach in comparison with(More)
The community detection in a social network has been become a key issue to discover the most important organizations in networks. Thenceforth, various approaches are proposed to resolve this inference problem. However, the applicability of these existing methods is trapped by their computational cost. In this paper, we propose a promising approach based on(More)
The enumeration of spanning trees in a finite graph is an important problem related to various domains of mathematics, physics and network reliability that has been investigated by many researchers. A network N is called a closed chain of planar networks if its modelling is defined by n planar graphs connected by articulation points. Some recent studies(More)
Graph theory is used to represent a communication network by expressing its linkage structure, the vertices represent objects and the pairs called edges or represent the interconnections between objects. The exact geometric positions of vertices or the lengths of the edges are not important. The purpose of this paper is to find a recursive relation counting(More)
The social network is a useful theoretical construction to study the relation between individuals, groups... The social network analysis is based on graph theory, in order to provide more opportunities to the participants to enlarge or make their social network more efficient. In this paper, we propose a promising approach based on the contraction of nodes(More)