2019

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Topological indices of complete t-partite graphs with applications in neural networks
(UMT Lahore, 2019-09) Aneeqa Aslam
Let be a collection of graphs and R be a set of real numbers. A mapping: R is called topological index if it associates each graph of to a unique real no of R. Let G1, G2, G3 and Gt be the null graphs with cardinalities of their vertex-sets S1, S2, S3 …, and St respectively, where Si ≥ 1 for 1 ≤ i ≤ t. A graph G = KS1 S2 S3 … St is called a t-partite graph if it is obtained from G1, G2, G3 … Gt such that V(G) = V(G1) ∪ V(G2) ∪ V(G3) … ∪ V(Gt) and for uv ∈ V(G), uv ∈ E(G) if one end u of the edge uv is in some V(Gi) and the other end v of the edge uv is in some V(Gj), where 1 ≤ i, j ≤ t and i ≠ j. In this thesis, we compute various degree-based topological indices (TIs) of t-partite graphs (KS1 S2 S3 … St) in their general form. We also apply the obtained results on the neural networks to discuss their various properties.