Consider the set SG(Qk) of all graphs whose vertices are labeled with non-identity elements of the group Qk = Z2 so that there is an edge between vertices with labels a and b if and only if the vertex labeled a + b is also in the graph. Note that edges always appear in triangles, since a + b = c, b + c = a and a + c = b are equivalent statements for Qk. We define the random cubic sum graph SG(Q...

In this paper, we calculate the eccentric connectivity index and the eccentricity sequence of two infinite classes of fullerenes with 50 + 10k and 60 + 12k (k in N) carbon atoms.

In studying branching properties of alkanes, several numbering schemes for the edges of the associated hydrogen-suppressed graph were proposed based on the degrees of the end vertices of an edge [11]. To preserve rankings of certain molecules, some inequalities involving the weights of edges needed to be satisfied. Randić [11] stated that weighting all edges uv of the associated graph G by (d(u...

we derived explicit formulae for the eccentric connectivity index and wiener index of2-dimensional square-octagonal tuc4c8(r) lattices with open and closed ends. newcompression factors for both indices are also computed in the limit n-->∞.

Design of some crystal and quasicrystal networks, based on rhombellane tiling,is presented. [1,1,1]Propellane,is a synthesized organic molecule; its hydrogenated form, the bicyclo[1.1.1]pentane,may be represented by the complete bipartite graph K2,3 which is the smallest rhombellane. Topology of translational and radial structures involving rhombellanes is described in terms of vertex symbol, c...

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 ...

The Sombor index is one of the geometry-based descriptors, which was defined as $$\begin{aligned} SO(G)=\sum _{uv\in E(G)}\sqrt{d^{2}_{u}+d^{2}_{v}}, \end{aligned}$$ where $$d_{u}$$ (resp. $$d_{v}$$ ) denotes degree vertex u v) in G. In this note, we determine graphs among set with connectivity edge connectivity) at most k having maximum and minimum indices, solves an open problem on proposed b...