‎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...

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 ...

THE USE OF ELECTROCONVULSIVE THERAPY TO TREAT SCHIZOAFFECTIVE DISORDER IN A PATIENT WITH PACEMAKER: A CASE REPORT Martina Rojnic Kuzman, Vesna Medved, Vedran Velagic, Eleonora Goluza & Zoran Bradas Department of Psychiatry, University Hospital Centre Zagreb, Zagreb, Croatia Department of Cardiovascular Medicine, University Hospital Centre Zagreb, Zagreb, Croatia Department of Anesthesiology, Un...

Let $A(G)$ be the adjacency matrix and $D(G)$ diagonal of vertex degrees a simple connected graph $G$. Nikiforov defined $A_{\alpha}(G)$ convex combinations as $A_{\alpha}(G)=\alpha D(G)+(1-\alpha)A(G)$, for $0\leq \alpha\leq 1$. If $ \rho_{1}\geq \rho_{2}\geq \dots \geq \rho_{n}$ are eigenvalues (which we call $\alpha$-adjacency $G$), \alpha $-adjacency energy $G$ is $E^{A_{\alpha}}(G)=\sum_{i...

Abstract In this paper, we give various lower and upper bounds for the energy of graphs in terms several topological indices graphs: first general multiplicative Zagreb index, Randić zeroth-order redefined indices, atom-bond connectivity index. Moreover, obtain new certain graph invariants as diameter, girth, algebraic radius.

1Department of Pediatrics, University of Zagreb, School of Medicine, University Hospital Centre Zagreb, Zagreb, Croatia, 2Department of Obstetrics and Gynecology, University Hospital Merkur, Zagreb, Croatia, 3Department of Pediatric Surgery, University of Zagreb, School of Medicine, University Hospital Centre Zagreb, Zagreb, Croatia, 4Department of Anesthesiology, Mayo Clinic, 200 First St SW, ...

The first general Zagreb index of a graph $G$ is defined as the sum $\alpha$th powers vertex degrees $G$, where $\alpha$ real number such that $\alpha \neq 0$ and 1$. In this note, for > 1$, we present upper bounds involving chromatic clique numbers graph; an integer \geq 2$, lower bound independence graph.