Results 41 to 50 of about 412,655 (203)
Online graph exploration on trees, unicyclic graphs and cactus graphs [PDF]
Information Processing Letters, 2021 We study the problem of exploring all vertices of an undirected weighted graph that is initially unknown to the searcher. An edge of the graph is only revealed when the searcher visits one of its endpoints. Beginning at some start node, the searcher's goal is to visit every vertex of the graph before returning to the start node on a tour as short as ...
openaire +5 more sources
All unicyclic graphs of order n with locating-chromatic number n-3
Indonesian Journal of Combinatorics, 2021 Characterizing all graphs having a certain locating-chromatic number is not an easy task. In this paper, we are going to pay attention on finding all unicyclic graphs of order n (⩾ 6) and having locating-chromatic number n-3.
Edy Tri Baskoro, Arfin Arfin
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The Aα-spectral radius of complements of bicyclic and tricyclic graphs with n vertices
Special Matrices, 2021 Recently, the extremal problem of the spectral radius in the class of complements of trees, unicyclic graphs, bicyclic graphs and tricyclic graphs had been studied widely.
Chen Chaohui +2 more
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Unicyclic graphs with maximal energy [PDF]
, 2002 Let G be a graph on n vertices and let λ1,λ2,…,λn be its eigenvalues. The energy of G is defined as E(G)=|λ1|+|λ2|+⋯+|λn|. For various classes of unicyclic graphs, the graphs with maximal energy are determined.
Woo, Ching-Wah +2 more
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Independent Dominating Sets in Unicyclic Graphs [PDF]
, 2022 Wilf found the maximum number of independent dominating sets of a tree using algebraic methods, while Sagan gave an elementary proof. In this thesis, we maximize the number of independent dominating sets of unicyclic graphs, giving a new proof of a ...
Lopez, Rachel
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On the Maximum Sombor Index of Unicyclic Graphs with a Fixed Girth
Journal of Mathematics, 2022 Let G be a graph having the set of edges EG. Represent by dGu the degree of a vertex u of G. The Sombor (SO) index of G is defined as SOG=∑uv∈EGdGu2+dGv2. The length of a shortest cycle in a graph G is known as the girth of G.
B. Senthilkumar +5 more
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Some results on the Laplacian eigenvalues of unicyclic graphs [PDF]
, 2009 In this paper, we provide the smallest value of the second largest Laplacian eigenvalue for any unicyclic graph, and find the unicyclic graphs attaining that value.
Li, Jianxi +2 more
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Ordering graphs with large eccentricity-based topological indices
Journal of Inequalities and Applications, 2021 For a connected graph, the first Zagreb eccentricity index ξ 1 $\xi _{1}$ is defined as the sum of the squares of the eccentricities of all vertices, and the second Zagreb eccentricity index ξ 2 $\xi _{2}$ is defined as the sum of the products of the ...
Yunfang Tang, Xuli Qi
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On Minimum Wiener Polarity Index of Unicyclic Graphs with Prescribed Maximum Degree
Journal of Applied Mathematics, 2014 The Wiener polarity index of a connected graph G is defined as the number of its pairs of vertices that are at distance three. By introducing some graph transformations, in different way with that of Huang et al., 2013, we determine the minimum Wiener ...
Jianping Ou, Xing Feng, Saihua Liu
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Locating Eigenvalues of a Symmetric Matrix whose Graph is Unicyclic
Trends in Computational and Applied Mathematics, 2021 We present a linear-time algorithm that computes in a given real interval the number of eigenvalues of any symmetric matrix whose underlying graph is unicyclic.
R. O. Braga +2 more
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