‎The first multiplicative Zagreb index $Pi_1(G)$ is equal to the‎ ‎product of squares of the degree of the vertices and the second‎ ‎multiplicative Zagreb index $Pi_2(G)$ is equal to the product of‎ ‎the products of the degree of pairs of adjacent vertices of the‎ ‎underlying molecular graphs $G$‎. ‎Also‎, ‎the multiplicative sum Zagreb index $Pi_3(G)$ is equal to the product of‎ ‎the sum...

the first zagreb index $m_1$ of a graph $g$ is equal to the sum of squaresof degrees of the vertices of $g$. goubko proved that for trees with $n_1$pendent vertices, $m_1 geq 9,n_1-16$. we show how this result can beextended to hold for any connected graph with cyclomatic number $gamma geq 0$.in addition, graphs with $n$ vertices, $n_1$ pendent vertices, cyclomaticnumber $gamma$, and minimal $m...

Merkur Clinical Hospital, Zagreb University School of Medicine, Department of Internal medicine, Zagreb, 1Zadar General Hospital, Department of Nephrology and Dialysis, Zadar, 2Bjelovar General Hospital, Department of Internal medicine, Bjelovar, 3Dubrava University Hospital, Department of Nephrology, Zagreb, 4Dubrovnik General Hospital, Department of Internal medicine, Dubrovnik and 5Rijeka Un...

in this paper we study the zagreb index in bucket recursive trees containing buckets with variable capacities. this model was introduced by kazemi in 2012. weobtain the mean and variance of the zagreb index andintroduce a martingale based on this quantity.

Based on picture fuzzy sets (PFSs), we use a mathematical model to tackle such types of problems when person has opinions like yes, no, abstain, and refusal. The spherical is more flexible practical than the model, as it enhances space uncertainty. It broadens vague information evaluated by decision makers since graphs are pictorial representation information. Graphs tool represent network. To ...

The Zagreb indices are the oldest graph invariants used in mathematical chemistry to predict the chemical phenomena. In this paper we define the multiple versions of Zagreb indices based on degrees of vertices in a given graph and then we compute the first and second extremal graphs for them.

Let G be a graph. The first Zagreb polynomial M1(G, x) and the third Zagreb polynomial M3(G, x) of the graph G are defined as:     ( ) ( , ) [ ] e uv E G G x x d(u) + d(v) M1 , ( , )  euvE(G) G x x|d(u) - d(v)| M3 . In this paper, we compute the first and third Zagreb polynomials of Cartesian product of two graphs and a type of dendrimers.

In a study on the structure–dependency of the total π-electron energy from 1972, Trinajstić and one of the present authors have shown that it depends on the sums ∑ v∈V d(v) 2 and ∑ v∈V d(v) , where d(v) is the degree of a vertex v of the underling molecular graph G. The first sum was later named first Zagreb index and over the years became one of the most investigated graph–based molecular stru...

Reumatizam 2010. 57(2) 1Klinika za reumatske bolesti i rehabilitaciju Referentni centar MZSS RH za reumatoidni artritis Klinički bolnički centar Zagreb Kišpatićeva 12 10000 Zagreb 2Klinika za reumatologiju, fi zikalnu medicinu i rehabilitaciju Referentni centar MZSS RH za spondiloartropatije Klinička bolnica “Sestre milosrdnice” Vinogradska 29 10000 Zagreb SPONZORIRANO PRIOPĆENJE SPONSORED COMM...

In theoretical chemistry, the researchers use graph models to express the structure of molecular, and the Zagreb indices and multiplicative Zagreb indices defined on molecular graph G are applied to measure the chemical characteristics of compounds and drugs. In this paper, we present the exact expressions of multiplicative Zagreb indices for certain important chemical structures like nanotube,...