Extremal k-generalized quasi unicyclic graphs with respect to first and second Zagreb indices

Extremum Modified First Zagreb Connection Index ofn-Vertex Trees with Fixed Number of Pendent Vertices

“…ese two Zagreb indices have several chemical applications, for example, see the recent papers [3,4]. Detail about the mathematical properties of the indices M 1 and M 2 can be found in the recent survey papers [5][6][7][8], recent papers [9][10][11][12][13][14][15][16][17][18][19][20][21][22], and related references listed therein.…”

“…Let us denote φ 1 (n, n 1 ): � 4n + 3n 2 1 − 9n 1 − 4 and φ 2 (n, n 1 ): � n 1 (2n − n 1 − 3). Now, by applying induction on n 1 , we show that if T ∈ T n,n 1 for n 1 ≥ 3, then (14) and (15) hold and the equalities in ( 14) and ( 15) hold only if T ∈ T n n 1 and T � K n n 1 , respectively. Let n 1 � 3, then T is a starlike tree and n ≥ 5.…”

The maximal tree with respect to the exponential of the second Zagreb index

“…The second Zagreb index was found to occur in certain approximate expressions of the total π-electron energy of alternant hydrocarbons [10]. We encourage the reader to consult [1,4,5,6,7,8,11,15] for the historical background, computational techniques, and mathematical properties of the second Zagreb index.…”

Comparison of Wiener index and Zagreb eccentricity indices

“…These two classical topological indices reflect the extent of branching of the molecular carbon-atom skeleton [22]. See [3,14,17,28,35,37] for various recent results on Zagreb indices. In analogy with the first and the second Zagreb index, Vukičević and Graovac [23] introduced the first and the second Zagreb eccentricity index as…”