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The degree of an edge uv is defined as the number of edges incident on vertices u and v other than itself. The Platt number of a graph is the sum of degrees of all its edges. In this paper, the concept of degree of an edge is analysed in social networks. The Platt number is investigated in certain classes of graphs and their total graphs. Also related bounds are proposed on connected graphs. An algorithm developed to determine the Platt number of any connected graph is presented. AMS Subject Classification: 05C10

PLATT NUMBER OF TOTAL GRAPHS