• Varshiki Jethwani
• Dr. R.P. Somani

Insects are invertebrate species of the Insecta class, within the Phylum Arthropoda, the largest and (on land) most widely distributed taxon. More than half (approximately 57 percent) of all animal species known are insects, and some authorities claim that less than 10 percent of living insect species have actually been described and named. In this paper we have tried to discover a mathematical approach towards them. The insects are divided into 4 categories and their graphs called the Insectile graph are obtained for the first time. Adjacency Matrix of the graph and the corresponding eigen values are calculated. Various topological indices like first and second Zagreb index, modified and Redefined Zagreb index, Harmonic index and Inverse sum index are calculated.

Insects, Insectile Graph, Topological Indices, Spectral Properties, Adjacency matrix

"SPECTRAL AND TOPOLOGICAL CHARACTERISTICS OF INSECTILE GRAPH", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.10, Issue 6, page no.i35-i44, June-2023, Available :http://www.jetir.org/papers/JETIR2306806.pdf

"SPECTRAL AND TOPOLOGICAL CHARACTERISTICS OF INSECTILE GRAPH", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.10, Issue 6, page no. ppi35-i44, June-2023, Available at : http://www.jetir.org/papers/JETIR2306806.pdf