On Some Bounds of Degree Based Topological Indices for Total Graphs

In this paper, we discuss the concept of total graph and computed some topological indices. If Θ is a simple graph, then the elements of Θ are the vertices ΘV and edges ΘE. For e=uu∈ ΘE, the vertex u and edge e, as well as u and e, are incident. We define the general harmonic $(GH)$ index and general sum connectivity $(GS)$ index for graph Θ regarding incident vertex-edge degrees as: Hₛα(Θ)=∑_eu(2_u+ₑ)α and χ̂ₛα(Θ)=∑_eu(_u+ₑ)α, where α is any real number. In this article, we derive the closed formulas for a few standard graphs for $(GH)$ and $(GS)$ indices and then go on to calculate the lowest and the greatest general harmonic index, as well as the general sum-connectivity index, for various graphs that correspond to their total graphs.