Dounia Lotfi

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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)
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)
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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