The first general Zagreb index is defined as $M_1^lambda(G)=sum_{vin V(G)}d_{G}(v)^lambda$. The case $lambda=3$, is called F-index. Similarly, reformulated first general Zagreb index is defined in terms of edge-drees as $EM_1^lambda(G)=sum_{ein E(G)}d_{G}(e)^lambda$ and the reformulated F-index is $RF(G)=sum_{ein E(G)}d_{G}(e)^3$. In this paper, we compute the reformulated F-index for some grap...

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.

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.

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...

the first zagreb index, $m_1(g)$, and second zagreb index, $m_2(g)$, of the graph $g$ is defined as $m_{1}(g)=sum_{vin v(g)}d^{2}(v)$ and $m_{2}(g)=sum_{e=uvin e(g)}d(u)d(v),$ where $d(u)$ denotes the degree of vertex $u$. in this paper, the firstand second maximum values of the first and second zagreb indicesin the class of all $n-$vertex tetracyclic graphs are presented.

Inspired by the chemical applications of higher-order connectivity index (or Randic index), we consider here the higher-order first Zagreb index of a molecular graph. In this paper, we study the linear regression analysis of the second order first Zagreb index with the entropy and acentric factor of an octane isomers. The linear model, based on the second order first Zag...

In this paper, the effects on the first general Zagreb index are observed when some operations, such as edge moving, edge separating and edge switching are applied to the graphs. Moreover, we obtain the majorization theorem to the first general Zagreb indices between two graphic sequences. Furthermore, we illustrate the application of these new properties, and obtain the largest or smallest fir...

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.