The Harary index of ordinary and generalized quasi-tree graphs

Xu, Kexiang; Wang, Jinlan; Liu, Hongshuang

doi:10.1007/s12190-013-0727-4

Cited by 20 publications

(8 citation statements)

References 16 publications

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“…The extremal value of many topological indices on quasi-tree graphs have been studied extensively, such as [5,9,[11][12][13][14]22]. However, there are few results on the topological indices of quasi-tree graphs with given graph parameters.…”

Section: Discussionmentioning

confidence: 99%

Quasi-Tree Graphs With Extremal General Multiplicative Zagreb Indices

Sun

2020

IEEE Access

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Zagreb indices and their modified versions of a molecular graph are important molecular descriptors which can be applied in characterizing the structural properties of organic compounds from different aspects. In this paper, by exploring the structures of the quasi-tree graphs with given different parameters (order, perfect matching and number of pendant vertices) and using the properties of the general multiplicative Zagreb indices, we determine the minimal and maximal values of general multiplicative Zagreb indices on quasi-tree graphs with given order, with perfect matchings, and with given number of pendant vertices. Furthermore, we present the minimal and maximal values of general multiplicative Zagreb indices on trees with perfect matchings. INDEX TERMS General multiplicative Zagreb indices, quasi-tree graph, tree, perfect matching, pendant vertex

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Section: Discussionmentioning

confidence: 99%

Quasi-Tree Graphs With Extremal General Multiplicative Zagreb Indices

Sun

2020

IEEE Access

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“…Lu in [14] has determined the Randić index of quasi trees. The Harary index of quasi tree graphs and generalized quasi tree graphs are presented in [18]. A strict k-quasi tree graph G is a connected graph which is not a tree, and k is the smallest positive integer such that there exists a k-element subset U of vertices for which G \ U is a tree.…”

Section: Introductionmentioning

confidence: 99%

On the Estrada Index of Point Attaching Strict k-Quasi Tree Graphs

Iranmanesh¹,

NEJATI²

2020

KgJMat

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Let G = (V, E) be a finite and simple graph with λ 1 , λ 2 ,. .. , λ n as its eigenvalues. The Estrada index of G is EE(G) = n i=1 e λi. For a positive integer k, a connected graph G is called strict k-quasi tree if there exists a set U of vertices of size k such that G \ U is a tree and this is as small as possible with this property. In this paper, we define point attaching strict k-quasi tree graphs and obtain the graph with minimum Estrada index among point attaching strict k-quasi tree graphs with k even cycles.

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“…Xu and Das [16] characterized the extremal bicyclic and unicyclic graphs for H(G). Xu et al [17] found the maximal H(G) for a fixed matching number on unicyclic graphs (for other example, see [1,2,3,6,7,9,10,11,12,13,15,18,19,20] and references cited therein).…”

Section: Introductionmentioning

confidence: 99%