In this paper we study lower bounds in a unified way for large family of topological indices, including the first variable Zagreb index M 1 ? . Our aim is to obtain sharp inequalities and characterize corresponding extremal graphs. The main results provide several vertex-degree-based indices. These are new even Zagreb, inverse forgotten

We investigate the Zagreb index, one of the topological indices, of random recursive trees in this paper. Through a recurrence equation, the first two moments of Zn, the Zagreb index of a random recursive tree of size n, are obtained. We also show that the random process {Zn − E[Zn], n ≥ 1} is a martingale. Then the asymptotic normality of the Zagreb index of a random recursive tree is given by...

1Čakovec General Hospital, Čakovec, Croatia; 2University Hospital Centre Zagreb, Department of Nephrology, Arterial Hypertension, Dialysis and Transplantation, Zagreb, Croatia; 3Sestre milosrdnice University Hospital Centre, Department of Nuclear Medicine, Zagreb, Croatia; 4University Hospital Centre Zagreb, Department of Dermatology and Venereology, Zagreb, Croatia; 5University of Zagreb Schoo...

Professor Željko Reiner, FRCP (London), FESC, FACC gained his MD degree in 1976 from Zagreb University, Croatia. He also holds a PhD degree from Zagreb University. Currently, he is the head of the Department of Internal Medicine, University Hospital Centre Zagreb and the School of Medicine, Zagreb University. He has held many positions in the European Society of Cardiology (ESC) and European At...

The generalized hierarchical product of graphs was introduced by L. Barriére et al in 2009. In this paper, reformulated first Zagreb index of generalized hierarchical product of two connected graphs and hence as a special case cluster product of graphs are obtained. Finally using the derived results the reformulated first Zagreb index of some chemically important graphs such as square comb latt...

The first general Zagreb index is defined as Mλ 1 (G) = ∑ v∈V (G) dG(v) λ where λ ∈ R − {0, 1}. The case λ = 3, is called F-index. Similarly, reformulated first general Zagreb index is defined in terms of edge-drees as EMλ 1 (G) = ∑ e∈E(G) dG(e) λ and the reformulated F-index is RF (G) = ∑ e∈E(G) dG(e) 3. In this paper, we compute the reformulated F-index for some graph operations.

in this paper, a new molecular-structure descriptor, the general sum–connectivity co–index  is considered, which generalizes the first zagreb co–index and the general sum–connectivity index of graph theory. we mainly explore the lower and upper bounds in termsof the order and size for this new invariant. additionally, the nordhaus–gaddum–type resultis also represented.

The first Zagreb index M1 is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M2 is equal to the sum of the products of the degrees of pairs of adjacent vertices of the respective graph. In this paper we present the lower bound on M1 and M2 among all unicyclic graphs of given order, maximum degree, and cycle length, and characterize graphs for which th...

1 University Hospital for Tumors, Clinical Hospital Centre “Sestre Milosrdnice”, Zagreb, Croatia; 2 University of Zagreb School of Medicine, Department of Clinical Oncology, and University Hospital Center Zagreb, Oncology Clinic, Zagreb, Croatia; 3 University of Zagreb School of Medicine, Department of Clinical Oncology, and University Hospital for Tumors, Clinical Hospital Centre “Sestre Milos...

1 Department of Mathematics, Faculty of Civil Engineering, University of Zagreb, Kačićeva 26, 10000 Zagreb, Croatia 2 Faculty of Food Technology and Biotechnology, University of Zagreb, Pierottijeva 6, 10000 Zagreb, Croatia 3 Abdus Salam School of Mathematical Sciences, 68-B, New Muslim Town, Lahore 54600, Pakistan 4 Faculty of Textile Technology, University of Zagreb, Prilaz baruna Filipovića ...