8,846 research outputs found
Bounds on the arithmetic-geometric index
The concept of arithmetic-geometric index was recently introduced in chemical graph theory, but it has proven to be useful from both a theoretical and practical point of view. The aim of this paper is to obtain new bounds of the arithmetic-geometric index and characterize the extremal graphs with respect to them. Several bounds are based on other indices, such as the second variable Zagreb index or the general atom-bond connectivity index), and some of them involve some parameters, such as the number of edges, the maximum degree, or the minimum degree of the graph. In most bounds, the graphs for which equality is attained are regular or biregular, or star graphs.This research was supported by a grant from Agencia Estatal de Investigación (PID2019-106433GBI00/ AEI/10.13039/501100011033), Spain. The research of José M. RodrÃguez was supported by the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M in the line of Excellence of University Professors (EPUC3M23), and in the context of the V PRICIT (Regional Programme of Research and Technological Innovation)
Computing Reformulated First Zagreb Index of Some Chemical Graphs as an Application of Generalized Hierarchical Product of Graphs
The generalized hierarchical product of graphs was introduced by L.
Barri\'ere 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 lattice, hexagonal chain, molecular graph of truncated cube, dimer
fullerene, zig-zag polyhex nanotube and dicentric dendrimers are computed.Comment: 12 page
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