Spectra of unicyclic graphs
WebUnicyclic graphs are discussed in the context of graph orderings related to eigenvalues. Several theorems involving lexicographical ordering by spectral moments as well as the … WebMatrix-graph theory is a fascinating subject that ties together two seemingly unrelated branches of mathematics. Because it makes use of both the combinatorial properties and the numerical properties of a matrix, this area of mathematics is fertile ground for research at the undergraduate, graduate, and professional levels.
Spectra of unicyclic graphs
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WebMoreover, we prove that one class of unicyclic graphs are determined by their signless Laplacian spectra. 1. Introduction Throughout the paper, 𝐺 = ( 𝑉, 𝐸) is an undirected simple graph with 𝑛 vertices and 𝑚 edges. If 𝐺 is connected with 𝑚 = 𝑛 + 𝑐 − 1, then 𝐺 is called a 𝑐 - cyclic graph. WebA unicyclic graph is a simple connected graph in which the number of edges is equal to the number of vertices. In this paper, firstly, we give the A α -characteristic polynomial of the …
WebSearch within Zikai Tang's work. Search Search. Home; Zikai Tang WebJan 15, 2007 · In this paper, we study the spectral radius of unicyclic graphs with n vertices and diameter d. We determined graphs with the largest spectral radius among all the unicyclic graphs with n vertices and diameter d.
WebA unicyclic graph is a connected graph containing exactly one cycle (Harary 1994, p. 41). A connected unicyclic graph is therefore a pseudotree that is not a tree . Truszczyński … WebAbstract. Let U n g be the set of connected unicyclic graphs of order n and girth g. Let C ( T 1, T 2, …, T g) ∈ U n g be obtained from a cycle v 1 v 2 ⋯ v g v 1 (in an anticlockwise direction) by identifying V i with the root of a rooted tree T i of order n i for each i = 1, 2, …, g, where n i ≥ 1 and ∑ i = 1 g n i = n.
WebAug 28, 2024 · In this paper we will apply the tensor and its traces to investigate the spectral characterization of unicyclic graphs. Let be a graph and be the -th power (hypergraph) of . …
WebDiagrams of the 89 unicyclic graphs on eight vertices are given in the Ap-pendix of [33]. They are ordered lexicographically by spectral moments. For each graph the eigenvalues, the first six spectral moments and coefficients of the char-acteristic polynomial are given. ' Diagrams of the 240 unicyclic graphs on nine vertices are ordered lexico- bridget reilly bandWebApr 6, 2024 · For 0 ≤ α ≤ 1, Nikiforov proposed to study the spectral properties of the family of matrices Aα(G) = αD(G) + (1− α)A(G) of a graph G, where D(G) is the degree diagonal matrix and A(G) is ... bridge trial wikiWebIn this paper, completely regular endomorphisms of unicyclic graphs are explored. Let G be a unicyclic graph and let c E n d ( G ) be the set of all completely regular endomorphisms … bridget reilly therapistWebChromatic spectrum of a colored graph G is a multiset of eigenvalues of colored adjacency matrix of G. The nullity of a disconnected graph is equal to sum of nullities of its components but we show that this result does not hold for colored graphs. In this paper, we investigate the chromatic spectrum of three different classes of 2-regular ... bridget richey lawrenceburg indianaWebAug 28, 2024 · The spectrum of $G$ is referring to its adjacency matrix, and the spectrum of $G^m$ is referring to its adjacency tensor. The graph $G$ is called determined by high-ordered spectra (DHS for... bridget regan the company you keepWebNov 1, 2014 · In Sections 3.1 and 3.2, we consider the graphs whose complement is connected (precisely a tree or a unicyclic graph, respectively) and characterize the graphs among them with n + 1 as the second smallest distance Laplacian eigenvalue. The following result describes the structure of a Fiedler vector of a tree. Theorem 1.2 (See [8].) bridget regan tv showsWebcospectral invariants of unicyclic graphs. We prove that a class of unicyclic graphs with cospectral mates is DHS, and give two examples of in nitely many pairs of cospectral unicyclic graphs but with di erent high-ordered spectra. 1. Introduction The graph isomorphism problem is one of few standard problems in computational complexity theory can voldemort fly