Some results on augmented Zagreb index of some trees and unicyclic graphs
Copyright policy )Some results on augmented Zagreb index of some trees and unicyclic graphs
Summary: The augmented Zagreb index (AZI) of a graph \(G\) is defined as \[\operatorname{AZI}(G) =\sum_{uv\in E(G)}\left(\frac{d_ud_v}{d_u+d_v-2}\right)^3, \] where \(E(G)\) and \(d_u\) denote set of edges of \(G\) and degree of the vertex \(u\) in \(G\) respectively. In this paper we establish some general results and bounds of AZI for certain unicyclic graphs and their corresponding chemical representation. We also obtain some results pertaining to AZI of certain trees.
Extremal problems in graph theory, Graphical indices (Wiener index, Zagreb index, Randić index, etc.), Chemical graph theory, AZI, Structural characterization of families of graphs, Vertex degrees, Molecular structure (graph-theoretic methods, methods of differential topology, etc.), unicyclic graph, Planar graphs; geometric and topological aspects of graph theory, tree
Extremal problems in graph theory, Graphical indices (Wiener index, Zagreb index, Randić index, etc.), Chemical graph theory, AZI, Structural characterization of families of graphs, Vertex degrees, Molecular structure (graph-theoretic methods, methods of differential topology, etc.), unicyclic graph, Planar graphs; geometric and topological aspects of graph theory, tree
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