The Gutman Index of the Unicyclic Graphs with pendent edges

Feng, Mengmeng; Yu, Xiangran; Zhang, Jing; Duan, Wei

doi:10.1088/1742-6596/2012/1/012053

Cited by 3 publications

(2 citation statements)

References 3 publications

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“…In fact, the Gutman index might be better called ZZ -index, for which we refer a paper [7] by Gutman that stated some facts about the history of the index. Bounds on the Gutman index for graphs with maximum degree and minimum degree were studied in [1,9], for unicyclic graphs were studied in [4,5]. Some methods for calculating the Gutman index were studied in [2].…”

Section: The Gutman Index Gutmentioning

confidence: 99%

Extremal General Gutman Index of Trees

Cheng¹,

Li²

2023

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The general Gutman index was introduced by Das and Vetrík very recently. For a graph G, the general Gutman index is defined bywhere α, β ∈ R, DG(u, v) denotes the distance between u and v in G, and dG(u) and dG(v) denote the degrees of u and v in G, respectively. We show that for some α and β, the general Gutman index decrease or increase with changing the adjacency of vertices.For some α and β, we characterize trees of given order with the largest or the smallest general Gutman index.

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Section: The Gutman Index Gutmentioning

confidence: 99%

Extremal General Gutman Index of Trees

Cheng¹,

Li²

2023

match

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“…Subsequently, it has been studied by numerous experts and scholars. In [4], Feng et al studied the Gutman index of unicyclic graphs with given pendant edges. The (vertex) degree distance and Gutman index of one vertex union of two cycles were given in [5,6], and new methods for calculating them were explored in [7].…”

Section: Introductionmentioning

confidence: 99%

The Vertex Gutman Index and Gutman Index of the Union of Two Cycles

Mei,

Miao

2024

Axioms

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The Wiener index is one of the most classic and widely used indicators in topology. It reflects the average distance of any node pair in the graph. It not only makes the boundaries of given graphs clearer but also continuously generates topological indices that are more suitable for new fields, such as the Gutman index. The Wiener index and Gutman index are two important topological indices, which are commonly used to describe the characteristics of molecular structure. They are closely related to the physical and chemical properties of molecular compounds. And they are widely used to predict the physical and chemical properties and biological activity of molecular compounds. In this paper, we study the vertex Gutman index and Gutman index and describe the structural characteristics of all cases of two simple cycles intersecting. We comprehensively analyze the Gutman index and vertex Gutman index in these cases in detail by means of classification discussion and analogical reasoning and characterize their maximum and minimum accordingly.

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Minimizing the Gutman Index among Unicyclic Graphs with Given Matching Number

Liu

Wang²

2023

Symmetry

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For a connected graph G with vertex set V, denote by d(v) the degree of vertex v and d(u, v) the distance between u and v. The value Gut(G)=∑{u,v}⊆Vd(u)d(v)d(u,v) is called the Gutman index of G. Recently, the graph minimizing the Gutman index among unicyclic graphs with pendent edges was characterized. Denoted by U(n,m) the set of unicyclic graphs on n vertices with matching number m. Motivated by that work, in this paper, we obtain a sharp lower bound for Gutman index of graphs in U(n,m), and the extremal graph attaining the bound is also obtained. It is worth noticing that all the extremal graphs are of high symmetry, that is, they have large automorphic groups.

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The Gutman Index of the Unicyclic Graphs with pendent edges

Cited by 3 publications

References 3 publications

Extremal General Gutman Index of Trees

Extremal General Gutman Index of Trees

The Vertex Gutman Index and Gutman Index of the Union of Two Cycles

Minimizing the Gutman Index among Unicyclic Graphs with Given Matching Number

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