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Exploring Caterpillar Tree Graph Topological Indices for Chemical Compound Prediction

Understand the significance of caterpillar tree graph topological indices in predicting chemical compound properties. Discover various distance-based and degree-based indices, including the Zagreb and Randic indices, and the novel F-index introduced by Furtula and Gutman.

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Exploring Caterpillar Tree Graph Topological Indices for Chemical Compound Prediction

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  1. DISTANCE BASED TOPOLOGICAL INDICES OF CATERPILLAR TREE GRAPH

  2. In graphtheory, a caterpillarorcaterpillartreeis a tree in whichallthevertices are withindistance 1 of a central path. Fortwovertices u &v n a graph G, thedistancefrom u to v isdenotedby d (u, v) & defined as thelengthof a shortest u-v path in graph G.

  3. Topological graph indices are widely used in mathematical chemistry to predict properties of chemical compounds. They have been intensively studied in recent years. Dozens of various indices were suggested to describe topology of complex molecules, among the earliest and the most famous being the first and the second Zagreb indices – M1 and M2 respectively.

  4. Many different topological indices have been investigated so far. Most of the useful topological indices are distance based or degree based. The Wiener index, the Harary index and the total eccentricity index are examples ofdistance based topological indices and the Zagreb indices and Randic index are examples of degree based topological indices.

  5. The popular research problem is to find the degree topological indices of the caterpillar tree graph, Depending on the degree sum of the vertices of a graph G and Z2(G) = and Followed by the rst Zagreb index, Furtula and Gutman introduced forgotten topological index (also called F-index) which was denfined as Z3(G) =

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