The aim of this paper is using the majorization technique to identify the classes of trees with extermal (minimal or maximal) value of some topological indices, among all trees of order n ≥ 12

The coprime graph of a group G is Γ_G with its set vertices and any two distinct are adjacent if only their order relatively prime. Let p be prime number, then G_p denotes the multiplicative 2×2 upper unitriangular matrices over ring integers modulo p. purposes this research to study Γ_(G_p ) find first second Zagreb eccentricity indices for p≥3. results as follows. First index )isE_1 (Γ_(G_p )...

Abstract. For a (molecular) graph G with vertex set V (G) and edge set E(G), the first and second Zagreb indices of G are defined as M1(G) = ∑ v∈V (G) dG(v) 2 and M2(G) = ∑ uv∈E(G) dG(u)dG(v), respectively, where dG(v) is the degree of vertex v in G. The alternative expression of M1(G) is ∑ uv∈E(G)(dG(u) + dG(v)). Recently Ashrafi, Došlić and Hamzeh introduced two related graphical invariants M...

Degree sequence measurements on graphs have attracted a lot of research interest in recent decades. Multiplying the degrees adjacent vertices graph Ω provides multiplicative first Zagreb index graph. In context theory, generalized is defined as product sum αth powers vertex Ω, where α real number such that α≠0 and α≠1. The focus this work extremal for several classes including trees, unicyclic,...

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.

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.

A topological index (TI) is a function that associates numeric number to the under-study molecular graph. The first TI based on distance was presented by Wiener find boiling point of paraffins. In 1972, compute total ? -electron energy molecule, degree-based indices are used. this paper, we obtained and second Zagreb con...

let $g$ be a graph and let $m_{ij}(g)$, $i,jge 1$, be the number of edges $uv$ of $g$ such that ${d_v(g), d_u(g)} = {i,j}$. the {em $m$-polynomial} of $g$ is introduced with $displaystyle{m(g;x,y) = sum_{ile j} m_{ij}(g)x^iy^j}$. it is shown that degree-based topological indices can be routinely computed from the polynomial, thus reducing the problem of their determination in each particular ca...

topological indices are numerical parameters of a graph which characterize its topology. inthis paper the pi, szeged and zagreb group indices of the tetrameric 1,3–adamantane arecomputed.