In this paper we give sharp upper bounds on the Zagreb indices and characterize all trees achieving equality in these bounds. Also, we give lower bound on first Zagreb coindex of trees.

Albertson [3] has defined the irregularity of a simple undirected graph G = (V,E) as irr(G) = ∑ uv∈E |dG(u)− dG(v)| , where dG(u) denotes the degree of a vertex u ∈ V . Recently, this graph invariant gained interest in the chemical graph theory, where it occured in some bounds on the first and the second Zagreb index, and was named the third Zagreb index [13]. For general graphs with n vertices...

Abstract The molecular descriptors are a useful tool in the spectral graph, chemistry and several fields of mathematics. edge F-index is proposed for fuzzy graphs (FGs) here. Bounds this index calculated FGs. FG has been investigated given set vertices as having maximum F-index. Some relations with second Zagreb hyper-Zagreb established. For an isomorphic FGs, it shown that value same. some ope...

Lea Milutinović1, Marijana Braš2,3, Veljko Đorđević3 1University of Zagreb School of Medicine, Student Society for Neuroscience, Zagreb, Croatia, 2Zagreb University Hospital Centre, Department of Psychological Medicine, Zagreb, Croatia, 3University of Zagreb School of Medicine, Centre for Palliative Medicine, Medical Ethics and Communication Skills, Zagreb, Croatia / 1Sveučilište u Zagrebu, Med...

School of Medicine, University of Zagreb, Croatia (VI, MJ); School of Medicine, University of Zagreb, Department of Nephrology, Hypertension, Dialysis and Transplantation, University Hospital Center Zagreb, Croatia (ML, AV, SK, JK, TZ, VP, MZ, BJ); School of Medicine, University of Zagreb, Department of Metabolic Disorders, University Hospital Center Zagreb, Zagreb, Croatia (IP); and School of ...

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...

‎Let G=(V,E) be a simple connected graph with vertex set V and edge set E. The first, second and third Zagreb indices of G are respectivly defined by: $M_1(G)=sum_{uin V} d(u)^2, hspace {.1 cm} M_2(G)=sum_{uvin E} d(u).d(v)$ and $ M_3(G)=sum_{uvin E}| d(u)-d(v)| $ , where d(u) is the degree of vertex u in G and uv is an edge of G connecting the vertices u and v. Recently, the first and second m...

<abstract><p>In this work we obtain new lower and upper optimal bounds of general Sombor indices. Specifically, get inequalities for these indices relating them with other indices: the first Zagreb index, forgotten index variable index. Finally, solve some extremal problems indices.</p></abstract>

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...