• Journal of applied mathematics & informatics
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• v.42 no.1
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• pp.159-167
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• 2024

The Topological indices are known as Mathematical characterization of molecules. In this paper, we have studied line graph of subdivision and semi-total point graph of triangular benzenoid, polynomino chains of 8-cycles and graphene sheet through forgotten and first Zagreb indices.

• The Pure and Applied Mathematics
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• v.27 no.4
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• pp.171-186
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• 2020

Long back in 1972, it was shown that the sum of the squares of vertex degrees and the sum of cubes of vertex degrees of a molecular graph both have large correlations with total 𝜋-electron energy of the molecule. Later on, the sum of squares of vertex degrees was named as first Zagreb index and became one of the most studied molecular graph parameter in the field of chemical graph theory. Whereas, the other sum remained almost unnoticed until recently except for a few occasions. Thus it got the name "forgotten" index or F-index. This paper investigates extremal graphs with respect to F-index among the class of bicyclic graphs with n vertices and k pendant vertices, 0 ≤ k ≤ n - 4. As consequences, we obtain the bicyclic graphs with largest and smallest F-indices.