Abstract
In this work, we study the degree-based topological invariants, and the general sum-connectivity, A B C 4 , G A 5 , general Zagreb, G A , generalized Randić, and A B C indices of the line graphs of some rooted product graphs ( C n { P k } and C n { S m + 1 } ) are determined by menas of the concept of subdivision. Moreover, we also computed all these indices of the line graphs of the subdivision graphs of i-th vertex rooted product graph C i , r { P k + 1 } .
Highlights
All graphs discussed in this paper are simple and connected
The subdivision of an edge uv in a graph G is deduced by inserting a new vertex w in V ( G ), and in edge set E( G ) the edge uv is replaced by two new edges uw and wv
The line graph L( G ) of a graph G is the graph with V ( L( E)) = E( G ), and e1 e2 ∈ E( L( G ))
Summary
All graphs discussed in this paper are simple and connected. Let G be a (molecular) graph with vertex set V ( G ) and edge set E( G ), respectively. Where α ∈ R (in what follows, α always denoted as a real number), and R−1/2 ( G ) is well known as Randić connectivity index of graph G. The Zagreb indices of the line graph with subdivision of these structure are studied in [17]. In light of graph structure analysis, Su and Xu [22] computed the general sum-connectivity index and co-index of the line graph of these graphs with subdivision. With the help of vertex and edge partitions, we compute various degree-based indices. 2. Topological Indices of Line Graph of the Subdivision Graph of Rooted Product of Graphs. In the theorem we will compute the general Zagreb index of the line graph of subdivision graph of Cn { Pk+1 }. In view of (1), (3), (4), and (6), we infer the required conclusions
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