A numerical quantity which characterize the whole structure of a graph is called a topological index. The concept of Randić (Rα), atom-bond connectivity (ABC) and geometric-arithmetic (GA) topological indices were established in chemical graph theory based on vertex degrees. In this paper, we study carbon nanotube network which is motivated by molecular structure of regular hexagonal lattice, and determine Rα, ABC and GA indices for this important class of networks.
Abstract:We study an edge irregular reflexive k-labelling for the generalized friendship graphs, also known as flowers (a symmetric collection of cycles meeting at a common vertex), and determine the exact value of the reflexive edge strength for several subfamilies of the generalized friendship graphs.
We introduce two new graph characteristics, the edge [Formula: see text]-irregularity strength and the vertex [Formula: see text]-irregularity strength of a graph. We estimate the bounds of these parameters and determine their exact values for several families of graphs namely, paths, ladders and fans.
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