TITLE:
The Maximum and Minimum Value of Exponential Randić Indices of Quasi-Tree Graph
AUTHORS:
Lei Qiu, Xijie Ruan, Yan Zhu
KEYWORDS:
Exponential Randić Index, Quasi-Tree Graph, Extremal Value, Extremal Graphs
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.12 No.5,
May
27,
2024
ABSTRACT: 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
e
1
d(
u
)d(
v
)
of all edges uv of G, where
d(
u
)
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.