الفهرس 
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Abstract
Graph theory has important applications in many real-world problems which can be represented with the help of graphs. The signi cance of the graph theory has been shown in the various areas of its contributions to various elds which include Biochemistry, Pure Mathematics, Computer Science, Operation Research, Sociology and other sciences. In this thesis, we give some modi cation results of Ma and Yao. The problem of counting the number of spanning trees of a network built by a replacement procedure that yields a self-similar structure is considered. This problem has been receiving growing attention in the specialized literature in recent years. One of the important measures of the global reliability of a network is the number of spanning trees. We also calculate the number of spanning trees in a class of the outerplanar, small world and self-similar fractal network models which can be constructed through graph operations and it has small-world and exponential free properties. Also, we get the entropy of the spanning trees of a class of self-similar fractals. The main result of this thesis is the generalization of the model proposed by Ma and Yao. By studying all the topological properties of the model such as clustering coe cient, degree distribution and average degree. The entropy of the proposed model is calculated. The Sierpi nski Gasket is one of the famous types of fractals, so we studied it to evaluate the explicit formula for some important top-structural indices of the two-dimensional base-3 Sierpi nski graph with any side length more than or equal to two.