TY - JOUR
T1 - Extremal k-generalized quasi trees for general sum-connectivity index
AU - Jamil, Muhammad Kamran
AU - Tomescu, Ioan
AU - Imran, Muhammad
N1 - Publisher Copyright:
© 2020, Politechnica University of Bucharest. All rights reserved.
PY - 2020
Y1 - 2020
N2 - For a simple graph G, the general sum-connectivity index is defined as χα(G) = ∑uv∈E(G) (d(u) + d(v))α, where d(u) is the degree of the vertex u and α ≠ 0 is a real number. The k-generalized quasi tree is a connected graph G with a subset Vk ⊂ V (G), where |Vk | = k such that G − Vk is a tree, but for any subset Vk−1 ⊂ V (G) with cardinality k − 1, G − Vk−1 is not a tree. In this paper, we have determined sharp upper and lower bounds of the general sum-connectivity index for α ≥ 1. The corresponding extremal k-generalized quasi trees are also characterized in each case.
AB - For a simple graph G, the general sum-connectivity index is defined as χα(G) = ∑uv∈E(G) (d(u) + d(v))α, where d(u) is the degree of the vertex u and α ≠ 0 is a real number. The k-generalized quasi tree is a connected graph G with a subset Vk ⊂ V (G), where |Vk | = k such that G − Vk is a tree, but for any subset Vk−1 ⊂ V (G) with cardinality k − 1, G − Vk−1 is not a tree. In this paper, we have determined sharp upper and lower bounds of the general sum-connectivity index for α ≥ 1. The corresponding extremal k-generalized quasi trees are also characterized in each case.
KW - Extremal graphs
KW - General sum-connectivity index
KW - K-quasi trees
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M3 - Article
AN - SCOPUS:85086080216
SN - 1223-7027
VL - 82
SP - 101
EP - 106
JO - UPB Scientific Bulletin, Series A: Applied Mathematics and Physics
JF - UPB Scientific Bulletin, Series A: Applied Mathematics and Physics
IS - 2
ER -