Graph theory can be used to optimize interconnection network systems. The compatibility of such networks mainly depends on their topology. Topological indices may characterize the topology networks. In this work, we studied a symmetric ?? formed by ? time repetition process joining ? copies selected graph ? in way that corresponding vertices all are joined with each other new edge. symmetry is ...

New graph invariants, named exponential Zagreb indices, are introduced for more than one type of index. After that, in terms lists on equality results over special graphs presented as well some new bounds unicyclic, acyclic, and general obtained. Moreover, these invariants determined operations.

zagreb indices belong to better known and better researched topological indices. weinvestigate here their ability to discriminate among benzenoid graphs and arrive at some quiteunexpected conclusions. along the way we establish tight (and sometimes sharp) lower andupper bounds on various classes of benzenoids.

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...

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 ...

For a (molecular) graph, the first Zagreb index M1 is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M2 is equal to the sum of the products of the degrees of pairs of adjacent vertices. It is well known that for connected or disconnected graphs with n vertices and m edges, the inequality M2/m ≥ M1/n does not always hold. Here we show that this relati...

Zagreb indices belong to better known and better researched topological indices. We investigate here their ability to discriminate among benzenoid graphs and arrive at some quite unexpected conclusions. Along the way we establish tight (and sometimes sharp) lower and upper bounds on various classes of benzenoids.

let g be a graph. the first zagreb m1(g) of graph g is defined as: m1(g) = uv(g) deg(u)2. in this paper, we prove that each even number except 4 and 8 is a first zagreb index of a caterpillar. also, we show that the fist zagreb index cannot be an odd number. moreover, we obtain the fist zagreb index of some graph operations.

The first Zagreb index M1 is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M2 is equal to the sum of the products of the degrees of pairs of adjacent vertices of the respective graph. In this paper we present the lower bound on M1 and M2 among all unicyclic graphs of given order, maximum degree, and cycle length, and characterize graphs for which th...

‎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...