Abstract:
This thesis investigates the properties of graph indices with a focus on the
extreme values of chemical trees with given order and branching vertices for
the maximum general sum-connectivity index and maximum general Sombor
index. For a graph G the general sum-connectivity and general Sombor
indices are respectively given by
χσ(G) = Σ (dG(p) + dG(q))σ and pq∈E(G) SOσ(G) = Σ (d2 G(p) + d2 G(q))σ. pq∈E(G)
Here dG(p) represents the degree of a vertex p in a graph G and E(G) is the
edge set of G.
Graph indices are numerical quantities that capture specific structural at
tributes of graphs and have significant implications in various fields like chem
istry, biology, and network analysis. The general sum-connectivity and gen
eral Sombor indices derived from the degrees of the vertices provide insights
into the connectivity of graphs. Research on the general sum-connectivity
index has been going on since 2010. However, the general Sombor index is
a newly developed topological index introduced by Hu, X. and Zhong, L. in
2022, which gained extensive attention due to its vast applicability. In this
thesis, we will determine the extremal values of general sum-connectivity and
general Sombor indices of chemical trees with the given order n and branch
ing vertices. By examining these indices, we aim to uncover patterns that
enhance our understanding of graph structures and their applications.
