WHY (A)? EXPLAIN ME PLEASE STEP BY STEP
Handshaking Theorem: This theorem says that, in any graph the sum of degree of all vertices is equal to the twice of number of edges in that graph.
Euler's Formula: The relation between number of vertices , number of edges and number of faces of a graph is
Consider a Fullerene graph with exactly pentagon and hexagon. Therefore total number of Faces are .
Let total number of vertices in the Fullerene graph are and total number of edges are . Since degree of each vertices in Fullerene graph is , therefore sum of degree of all vertices is , therefore applying Handshaking Theorem:
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