TY - JOUR
T1 - General Randić index of unicyclic graphs with given diameter
AU - Alfuraidan, Monther Rashed
AU - Das, Kinkar Chandra
AU - Vetrík, Tomáš
AU - Balachandran, Selvaraj
N1 - Publisher Copyright:
© 2021 Elsevier B.V.
PY - 2022/1/15
Y1 - 2022/1/15
N2 - We study the general Randić index Ra(G)=∑uv∈E(G)[degG(u)degG(v)]a, where a∈R, E(G) is the edge set of a graph G, and degG(u) and degG(v) are the degrees of vertices u and v, respectively. For a set of unicyclic graphs of given order and diameter, we present the unique graph having the minimum general Randić index, where −0.64≤a<0. Since [Formula presented] is the Randić index of a graph G, our result holds also for the classical Randić index.
AB - We study the general Randić index Ra(G)=∑uv∈E(G)[degG(u)degG(v)]a, where a∈R, E(G) is the edge set of a graph G, and degG(u) and degG(v) are the degrees of vertices u and v, respectively. For a set of unicyclic graphs of given order and diameter, we present the unique graph having the minimum general Randić index, where −0.64≤a<0. Since [Formula presented] is the Randić index of a graph G, our result holds also for the classical Randić index.
KW - Diameter
KW - General Randić index
KW - Unicyclic graph
UR - https://www.scopus.com/pages/publications/85116505286
U2 - 10.1016/j.dam.2021.09.016
DO - 10.1016/j.dam.2021.09.016
M3 - Article
AN - SCOPUS:85116505286
SN - 0166-218X
VL - 306
SP - 7
EP - 16
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
ER -