The exponential Randić index has important applications in the fields of biology and chemistry. The exponential Randić index of a graph G is defined as the sum of the weights
of all edges uv of G, where
denotes the degree of a vertex u in G. The paper mainly provides the upper and lower bounds of the exponential Randić index in quasi-tree graphs, and characterizes the extremal graphs when the bounds are achieved.
References
[1]
Bollobás, B. and Erdös, P. (1998) Graphs of Extremal Weights. Ars Combinatorial, 50, 225-233.
[2]
Hu, Y.M., Li, X.L. and Yuan, Y. (2004) Trees with Minimum General Randić Index. MATCH Communications in Mathematical and in Computer Chemistry, 52, 119-128.
[3]
Li, X.L., Shi, Y.T. and Xu, T.Y. (2006) Unicyclic Graphs with Maximum General Randic Index for alpha> 0. MATCH Communications in Mathematical and in Computer Chemistry, 56, 557-570.
[4]
Wu, B.Y.D.R. and Zhang, L. (2005) Unicyclic Graphs with Minimum General Randic Index. MATCH Communications in Mathematical and in Computer Chemistry, 54, 455-464.
[5]
Pavlović, L. (2003) Maximal Value of the Zeroth-Order Randić Index. Discrete Applied Mathematics, 127, 615-626. https://doi.org/10.1016/S0166-218X(02)00392-X
[6]
Li, X.L. and Zhao, H.X. (2004) Trees with the First Three Smallest and Largest Generalized Topological Indices. MATCH Communications in Mathematical and in Computer Chemistry, 50, 57-62.
[7]
Zhang, S.G. and Zhang, H.L. (2006) Unicyclic Graphs with the First Three Smallest and Largest First General Zagreb Index. MATCH Communications in Mathematical and in Computer Chemistry, 55, 427-438.
[8]
Jahanbani, A., Cancan, M. and Motamedi, R. (2022) Extremal Trees for the Exponential of Forgotten Topological Index. Journal of Mathematics, 2022, Article ID: 7455701. https://doi.org/10.1155/2022/7455701
[9]
Lu, M. and Gao, J.W. (2007) On the Randić Index of Quasi-Tree Graphs. Journal of Mathematical Chemistry, 42, 297-310. https://doi.org/10.1007/s10910-006-9089-6
[10]
Sun, X.L., Gao, Y.B. and Du, J.W. (2022) The Zeroth-Order Generalized Randić Index of Quasi-Tree Graphs. Journal of Shandong University (Natural Science), 57, 96-102.
