Abstract In this paper, we give various lower and upper bounds for the energy of graphs in terms several topological indices graphs: first general multiplicative Zagreb index, Randić zeroth-order redefined indices, atom-bond connectivity index. Moreover, obtain new certain graph invariants as diameter, girth, algebraic radius.

Porous material such as metal-natural constructions and their particular partner poly-hydra are made up of inorganic clusters with no saturation exhibit great capability for utilization in the absorption gas ascending opening optics detecting biotechnology hardware. Cuboctahedral bi-metallic structure is an often-quoted example polyhedra class. In this study, we have calculated first second Zag...

We study the most general conditions under which the computations of the index of a perturbed Dirac operator Ds = D + sZ localize to the singular set of the zeroth order operator Z in the semi-classical limit s → ∞. We use Witten’s method to compute the index of D by doing a combinatorial computation involving local data at the nondegenerate singular points of the operator Z. The paper contains...

We study the most general conditions under which the computations of the index of a perturbed Dirac operator Ds = D + sZ localize to the singular set of the zeroth order operator Z in the semi-classical limit s → ∞. We use Witten’s method to compute the index of D by doing a combinatorial computation involving local data at the nondegenerate singular points of the operator Z. The paper contains...

Several different topological indices (the carbon number, the Wiener index, the Balaban dis­ tance sum connectivity index, the Randic molecular identification number, and the Randic molecular connectivity indices °/, 2%, 3̂ p and 3/ c) were employed in the correlation of the velocity of ultrasonic sound in a variety of alkane and alcohol species. Using linear regression analyses and published so...

In this paper, we present some new lower and upper bounds for the modified Randic index in terms of maximum, minimum degree, girth, algebraic connectivity, diameter and average distance. Also we obtained relations between this index with Harmonic and Atom-bond connectivity indices. Finally, as an application we computed this index for some classes of nano-structures and linear chains.

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...

The Atom-bond-connectivity index ABC of a graph G is determined by d_i and d_j. In this paper, sharp results for the general which has chemical applications are found using different methods. These new inex investigated in terms its edges, vertices degrees. particular, some relations obtained involving topological indices; Randic index, Zagreb Harmonic Narumi-Katayama index. Indeed, improved he...

We prove that, for any graph G, its energy is at least twice the Randic index. show that equality holds if and only G union of complete bipartite graphs.