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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)
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)
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 Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract 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(More)
It is known that Kirchhoff Matrix Theorem computes the number of spanning trees in any graph G by taking a determinant; so far, many works derived a recursive function to calculate the complexity of certain families of maps specially Grid map. In this paper we give the major recursive formula that counts the number of spanning trees in the general case of(More)
During the last decade, the social networks have known a huge popularity due to their ease of connecting people. The community detection has been in the center of attention in the analysis of this kind of networks. However, this area is still a very active field of research; the majority of methods involving this problem suffers from the accuracy in the(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 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)
Enumeration of trees is a new line of research in graph theory; many researchers worked on this area, starting with the Matrix Tree Theorem given by Kirchhoff who defined the number of spanning trees in graph G as the determinant of its Laplacian matrix, since this later is easy to compute but it cannot give the recurrences of spanning trees. In this paper,(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)
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