Let G be a graph with vetex set V (G) and edge set E(G). The first generalized multiplicative Zagreb index of G is ∏ 1,c(G) = ∏ v∈V (G) d(v) , for a real number c > 0, and the second multiplicative Zagreb index is ∏ 2(G) = ∏ uv∈E(G) d(u)d(v), where d(u), d(v) are the degrees of the vertices of u, v. The multiplicative Zagreb indices have been the focus of considerable research in computational ...

In this note, we obtain the expressions for multiplicative Zagreb indices and coindices of derived graphs such as a line graph, subdivision graph, vertex-semitotal graph, edge-semitotal graph, total graph and paraline graph.

the chromatic number of a graph g, denoted by χ(g), is the minimum number of colors such that g can be colored with these colors in such a way that no two adjacent vertices have the same color. a clique in a graph is a set of mutually adjacent vertices. the maximum size of a clique in a graph g is called the clique number of g. the turán graph tn(k) is a complete k-partite graph whose partition...

The chromatic number of a graph G, denoted by χ(G), is the minimum number of colors such that G can be colored with these colors in such a way that no two adjacent vertices have the same color. A clique in a graph is a set of mutually adjacent vertices. The maximum size of a clique in a graph G is called the clique number of G. The Turán graph Tn(k) is a complete k-partite graph whose partition...

The study of the maximum and minimal characteristics graphs is focus significant field mathematics known as extreme graph theory. Finding biggest or smallest that meet specified criteria main goal this discipline. There are several applications extremal theory in various fields, including computer science, physics, chemistry. Some important include: Computer networking, social chemistry physics...

For a graph $G$ with edge set $E(G)$, the multiplicative sum Zagreb index of $G$ is defined as$Pi^*(G)=Pi_{uvin E(G)}[d_G(u)+d_G(v)]$, where $d_G(v)$ is the degree of vertex $v$ in $G$.In this paper, we first introduce some graph transformations that decreasethis index. In application, we identify the fourteen class of trees, with the first through fourteenth smallest multiplicative sum Zagreb ...