TITLE:
On the Degree Resistance Distance of Unicyclic Graphs
AUTHORS:
Kun Wang, Wenjie Ning
KEYWORDS:
Degree Resistance Distance, Unicyclic Graph, Resistance Distance, Kirchhoff Index
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.12 No.11,
November
6,
2024
ABSTRACT: Let
G
be a connected graph with vertex set
V(
G
)
. Then the degree resistance distance of
G
is defined as
D
R
(
G
)=
∑
{
u,v }⊆V(
G
)
(
d(
u
)+d(
v
)
)R(
u,v
)
, where
d(
u
)
is the degree of the vertex
u
, and
R(
u,v
)
is the degree resistance distance between
u
and
v
in graph
G
. A unicyclic graph is a connected graph with a unique cycle. In this paper, we characterize the unique graph with the third-maximum degree resistance distance among all unicyclic graphs with
n
vertices.