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Recently, Wang et al. (2017) introduced two new operations of graphs. In this paper we establish explicit expressions of some Zagreb indices viz. first Zagreb index, second Zagreb index and forgotten topological index of these two newly proposed operations of graphs. Then as an application we further establish explicit formulae of some other topological indices of the two operations of graphs.

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Background: Fine needle aspiration is currently the preferred screening test for guiding the diagnosis and treatment of thyroid nodules as it is quick, assessible, inexpensive, relatively painless with quite accurate diagnosis. The Bethesda system for reporting thyroid cytopathology (TBSRTC) was introduced in 2007 in an attempt to standardize international terminology and to categorize morphological criteria in ne-needle aspirations (FNAs) from patients with thyroid nodules. It introduced 6 diagnostic categories for FNA results and assigns a malignancy risk and recommendations for patient management for each category. To categorize theObjectives: thyroid swelling following The Bethesda system for reporting Thyroid Cytopathology (TBSRTC) and to correlate with nal histopathological reports wherever available. : 99 patients underwent FNAC in our institute from the period of January 2019 to July 2020,Materials and Methods and were categorized according to the Bethesda system for reporting thyroid cytopathology. Results: The 99 cases taken up for FNAC were categorized according to The Bethesda system for reporting Thyroid Cytopathology (TBSRTC) as Non-diagnostic or unsatisfactory at 6.06%, Benign at 81.81%, Atypia of undetermined signicance at 0%, Suspicious for a follicular neoplasm at 4.04%, Suspicious for malignancy at 2.02%, Malignant at 6.06%. The sensitivity, specicity, positive predictive value (PPN), negative predictive value (NPN), and accuracy of FNAC in diagnosing thyroid malignancy were calculated as 66.67%, 100%, 100%, 93.33% and 94.12% respectively. The BethesdaConclusion: system for reporting Thyroid Cytopathology (TBSRTC) helps in standardization of thyroid ne needle aaspiration reporting. This leads to timely and adequate intervention for the patient and also minimizes unnecessary thyroid surgeries