The generalized hierarchical product of graphs was introduced by L. Barriére et al in 2009. In this paper, reformulated first Zagreb index of generalized hierarchical product of two connected graphs and hence as a special case cluster product of graphs are obtained. Finally using the derived results the reformulated first Zagreb index of some chemically important graphs such as square comb latt...

In this paper, we introduce two combinatorial operations and a knot-theoretical approach for generation and description of fullerene architectures. The ‘Spherical rotating–vertex bifurcation’ operation applied to original fullerene polyhedra can lead to leapfrog fullerenes. However, the ‘Spherical stretching–vertex bifurcation’ operation applied to fullerene generates a family of related polyhe...

Fullerenes are molecules of carbon that are modeled by trivalent plane graphs with only pentagonal and hexagonal faces. Scaling up a fullerene gives a notion of similarity, and fullerenes are partitioned into similarity classes. In this expository article, we illustrate how the values of two important fullerene parameters can be deduced for all fullerenes in a similarity class by computing the ...

The smallest number of edges that have to be deleted from a graph G to obtain a bipartite spanning subgraph is called the bipartite edge frustration of G and denoted by φ(G). In this paper our recent results on computing this quantity for hierarchical product of graphs are reported. We also present a fast algorithm for computing edge frustration index of (3, 6)−fullerene graphs.

Two definitions of the problem of graph drawing are considered, and an analytical solution is provided for each of them. The solutions obtained make use of the eigenvectors of the Laplacian matrix of a related structure. The procedures give good results for symmetrical graphs, and they have already been used for drawing fullerene molecules in the literature. The analysis characterizes precisely...