enumeration of the number of spanning trees in some ... - Toubkal

18 LIST OF TABLESspecial panar maps. We were able to obtain explicit simple formulae for calculating thenumber of spanning trees in some special planar maps.The results of Chapter 6 are published in article [86]. In this paper, we have beeninterested in calculating the number of spanning trees in the star flower planar map andhave derived the explicit formula to calculate the number of spanning trees in the starflower planar maps.The results of Chapter 7 were divided into two parts. The first part emphasizes uponthe determination of Weiner index in the case of planar maps, in general, and in maximalplanar maps particularly, as can be seen in [90]. While, the second part focuses on thederivation of an explicit formula to calculate the number of spanning trees in a maximalplanar map by employing the Laplacian matrix of planar maps (Matrix Tree Theorem)which has already been published in [84].