Spectra of unicyclic graphs
WebMay 3, 2024 · In particular, λ1 (G) is called the spectral radius of G, λn (G) is the least eigenvalue of G, and the spread of G is defined to be the difference between λ1 (G) and λn (G). Let U (n) be the set of... WebSep 3, 2014 · Abstract. Let be the unicyclic graph with vertices obtained by attaching two paths of lengths and at two adjacent vertices of cycle .Let be the unicyclic graph with vertices obtained by attaching paths of lengths at the same vertex of cycle .In this paper, we prove that and are determined by their Laplacian spectra when is even.. 1. Introduction. …
Spectra of unicyclic graphs
Did you know?
WebNov 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].) WebAug 26, 2016 · On Unicyclic Graphs Spectra: New Results Abstract: Let G = (V, E) be a unicyclic simple undirected graph. In this paper, we investigate the spectra of a particular …
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 … WebAug 28, 2024 · High-ordered spectral characterization of unicyclic graphs. Yi-Zheng Fan, Hong-Xia Yang, Jian Zheng. 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 . The spectrum of is referring to its adjacency matrix, and the …
WebThe least ϵ -eigenvalue of unicyclic graphs. Let ξ i 1 > ξ i 2 > ⋯ > ξ i k be all the distinct ϵ -eigenvalues of a connected graph G. Then the ϵ -spectrum of G can be written as S p e c ϵ ( G) = ξ i 1 ξ i 2 … ξ i k m 1 m 2 … m k, where m j is the multiplicity of the eigenvalue ξ i … WebChromatic 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 ...
WebApr 1, 2024 · On the ABC spectra radius of unicyclic graphs. Article. Mar 2024; LINEAR ALGEBRA APPL; ... In this paper, we prove that for a unicyclic graph G of order n≥4,2=ν1(Cn)≤ν1(G)≤ν1(Sn+e), with ...
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 … thema fotograafWebA 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 (1984) conjectured that all unicyclic graphs except the cycle graph with … tide forecast orange beach alWebDec 15, 2024 · The Aα -spectral radius of unicyclic graphs The special unicyclic graph U D * has been introduced by Zhang [14]. For a given nonincreasing unicyclic graphic sequence D = ( d 0, d 1, …, d n − 1) with n ≥ 3, U D * = C n if d 0 = 2 obviously. Next, we assume that d0 ≥ 3. Set G 3 = C 3 = v 0 v 1 v 2 v 0. thema fotoWebJan 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. tide forecast port aransasWebMar 26, 2024 · As an application, we determine signed graphs that maximize the spectral radius in the class of unicyclic signed graphs with fixed order and girth. We also give certain upper bounds on the... thema fotografie kleutersWebA 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 … tide forecast philippinesWebJul 1, 2024 · A unicyclic graph is a simple connected graph with equal number of vertices and edges. Obviously, a unicyclic graph contains a unique cycle. The adjacency matrix of … thema foute party