TY - JOUR

T1 - Extremal k-generalized quasi trees for general sum-connectivity index

AU - Jamil, Muhammad Kamran

AU - Tomescu, Ioan

AU - Imran, Muhammad

N1 - Funding Information:
This research is supported by the UPAR Grant of United Arab Emirates, Al-Ain, UAE via Grant No. G00002590.
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 -