Sharp Bounds of the Hyper-Zagreb Index on Acyclic, Unicylic, and Bicyclic Graphs
2017 ◽
Vol 2017
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pp. 1-5
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Keyword(s):
The hyper-Zagreb index is an important branch in the Zagreb indices family, which is defined as∑uv∈E(G)(d(u)+d(v))2, whered(v)is the degree of the vertexvin a graphG=(V(G),E(G)). In this paper, the monotonicity of the hyper-Zagreb index under some graph transformations was studied. Using these nice mathematical properties, the extremal graphs amongn-vertex trees (acyclic), unicyclic, and bicyclic graphs are determined for hyper-Zagreb index. Furthermore, the sharp upper and lower bounds on the hyper-Zagreb index of these graphs are provided.
2016 ◽
Vol 08
(03)
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pp. 1650040
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Keyword(s):
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2020 ◽
Vol 23
◽
2015 ◽
Vol 92
(2)
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pp. 177-186
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Keyword(s):
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2010 ◽
Vol 158
(17)
◽
pp. 1953-1962
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Keyword(s):
2020 ◽
Vol 12
(05)
◽
pp. 2050068
Keyword(s):
2009 ◽
Vol 3
(2)
◽
pp. 371-378
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Keyword(s):