in this survey article a brief account on the development of padmakar-ivan (pi) index in thatapplications of padmakar-ivan (pi) index in the fascinating field of nano-technology arediscussed.

in this paper, at first we introduce a new index with the name co-pi index and obtain someproperties related this new index. then we compute this new index for tuc4c8(r) nanotubes.

the unitary cayley graph xn has vertex set zn = {0, 1,…, n-1} and vertices u and v areadjacent, if gcd(uv, n) = 1. in [a. ilić, the energy of unitary cayley graphs, linear algebraappl. 431 (2009) 1881–1889], the energy of unitary cayley graphs is computed. in this paperthe wiener and hyperwiener index of xn is computed.

the rice conversion process is an agricultural transformative industry that consumes a great deal of fossil fuel and electricity. in this study, the effect of different factors on energy consumption, energy consumption index and whitening index were investigated. the experimental design was a split plot design with four whitening periods (15, 30, 45, 60s) (main plot), three rice varieties (khaz...

rheological characteristics of al2o3, cuo and tio2 nano particles were investigated in oil asthe base fluid at 1 and 2 wt.%. constitutive relations for non-newtonian fluid were discussedbased on the power-law model. measured viscosities of each nanofluid were used to evaluatethe power-law and consistency index. results indicated that the nanofluid viscosity decreasedby increasing the concentrat...

hansen et‎. ‎al.‎, ‎using the autographix software ‎package‎, ‎conjectured that the szeged index $sz(g)$ and the‎ ‎wiener index $w(g)$ of a connected bipartite graph $g$ with $n geq ‎4$ vertices and $m geq n$ edges‎, ‎obeys the relation‎ ‎$sz(g)-w(g) geq 4n-8$‎. ‎moreover‎, ‎this bound would be the best possible‎. ‎this paper offers a proof to this conjecture‎.

the total irregularity of a graph g is defined as 〖irr〗_t (g)=1/2 ∑_(u,v∈v(g))▒〖|d_u-d_v |〗, where d_u denotes the degree of a vertex u∈v(g). in this paper by using the gini index, we obtain the ordering of the total irregularity index for some classes of connected graphs, with the same number of vertices.

the atom-bond connectivity index of graph is a topological index proposed by estrada et al.as abc (g)  uve (g ) (du dv  2) / dudv , where the summation goes over all edges ofg, du and dv are the degrees of the terminal vertices u and v of edge uv. in the present paper,some upper bounds for the second type of atom-bond connectivity index are computed.

symmetric division deg index is one of the 148 discrete adriatic indices that showed good predictive properties on the testing sets provided by international academy of mathematical chemistry.symmetric division deg index is defined by$$sdd(g) = sume left( frac{min{d_u,d_v}}{max{d_u,d_v}} + frac{max{d_u,d_v}}{min{d_u,d_v}} right),$$where $d_i$ is the degree of vertex $i$ in graph $g$.in this pap...