Unicyclic graphs with extremal values of arithmetic–geometric index

Bounds for the geometric-arithmetic index of unicyclic graphs

“…A connected graph G is called a unicyclic graph if it contains exactly one cycle. In [10], Vukićević, Vujošević, and Popivoda computed the lower and upper bounds for the AG index of unicyclic graphs and proved that the bounds are sharp by providing the extremal graphs for the corresponding bounds. Our goal is to find the lower and upper bounds for the GA index of a unicyclic graph G and the extremal graphs for the corresponding bounds, that is, we show that…”

“…where n is the number of vertices of the graph G. The extremal graph for the upper bound is the cycle graph C n and the extremal graph for the lower bound is the graph obtained by attaching n − 3 pendant vertices to a vertex of the cycle graph C 3 . We follow the definitions and notations in [10]. A vertex v is called a cycle vertex if it lies on the cycle of G and an edge e is called a cycle edge if it is an edge of the cycle of G. A cycle vertex v is called a local maximum vertex if the degree of v is greater than or equal to the degree of its neighbor cycle vertices, that is,…”

Relations Between Arithmetic-Geometric Index And Geometric-Arithmetic Index

“…A lot of research has been done on both indices. The AG index was investigated for example in [10], [11] and [13], and the GA index in [3], [6], [12] and [15]. Chemical applications of the GA index were studied for instance in [1], [17] and [19], and many interesting results can be found in the survey paper [8].…”