Results 41 to 50 of about 298 (175)
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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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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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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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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On Unicyclic Graphs Spectra: New Results
2016 IEEE Intl Conference on Computational Science and Engineering (CSE) and IEEE Intl Conference on Embedded and Ubiquitous Computing (EUC) and 15th Intl Symposium on Distributed Computing and Applications for Business Engineering (DCABES), 2016 Let G = (V, E) be a unicyclic simple undirected graph. In this paper, we investigate the spectra of a particular class of unicyclic graphs G(q, n1) where q is the size of the unique cycle. Each vertex of the unique cycle is attached to n1 vertices. We provide the " exact values " of the extremal eigenvalues of the adjacency matrix A and the Laplacian ...
Hadji, Makhlouf, Chau, Ming
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The Laplacian Spectral Radius of a Class of Unicyclic Graphs
Journal of Applied Mathematics, 2013 Let C(n,k) be the set of all unicyclic graphs with n vertices and cycle length k. For any U∈C(n,k), U consists of the (unique) cycle (say Ck) of length k and a certain number of trees attached to the vertices of Ck having (in total) n-k edges.
Haixia Zhang
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Journal of Applied Mathematics, 2012 Let Φ(G,λ)=det(λIn-L(G))=∑k=0n(-1)kck(G)λn-k be the characteristic polynomial of the Laplacian matrix of a graph G of order n. In this paper, we give four transforms on graphs that decrease all Laplacian coefficients ck(G) and investigate a conjecture A.
Xinying Pai, Sanyang Liu
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Zagreb Indices of Trees, Unicyclic and Bicyclic Graphs With Given (Total) Domination
IEEE Access, 2019 Let G = (V, E) be a (molecular) graph. For a family of graphs G, the first Zagreb index M1 and the second Zagreb index M2 have already studied. In particular, it has been presented, the first Zagreb index M1 and the second Zagreb index M2 of trees T in ...
Doost Ali Mojdeh +3 more
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The Largest Laplacian Spectral Radius of Unicyclic Graphs with Fixed Diameter
Journal of Applied Mathematics, 2013 We identify graphs with the maximal Laplacian spectral radius among all unicyclic graphs with n vertices and diameter d.
Haixia Zhang
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Atom-bond connectivity index and diameter of graphs
Journal of Hebei University of Science and Technology, 2016 For further study of the numerous nice properties of topological indices in physical and chemical fields, it is worth considering the relation between a degree-based index and a distance-based index.
Lin WU, Yumei HU
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