On the abc spectra radius of unicyclic graphs
Web10 de out. de 2006 · The spread s(G) of a graph G is defined as s(G) = maxi,j λ i − λ j , where the maximum is taken over all pairs of eigenvalues of G. Let U(n,k) denote the set … Web15 de dez. de 2024 · The A α-spectral radius of unicyclic graphs. The special unicyclic graph U D * has been introduced by Zhang [14]. For a given nonincreasing unicyclic …
On the abc spectra radius of unicyclic graphs
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Webmine the unique graphs such that the di erence between the maximum degree and the -spectral radius is maximum among trees, unicyclic graphs and non-bipartite graphs, respectively. 2010 Mathematics Subject Classi cation: 05C50 Keywords and Phrases: -spectral radius, adjacency matrix, sign-less Laplacian matrix, tree, unicyclic graph, … WebIn the article, we consider the problem of characterization of connected graphs having exactly three distinct Laplacian ABC-eigenvalues. We solve this problem for bipartite graphs, multipartite graphs, unicyclic graphs, regular graphs and prove the non-existence of such graphs with diameter greater than 2.
Web15 de jan. de 2007 · AMS classification: 05C50; 15A18 Keywords: Unicyclic graph; Spectral radius; Diameter 1. Introduction Let G = (V, E) be a simple undirected graph … Web[25] Bao, Y.–H., Tan, Y.Y., Fan, Y.–Z.The Laplacian spread of unicyclic graphs. Appl. Math. Lett., 22 ( 2009 ), 1011–1015. Google Scholar [26] Bapat, R.B., Lal, A.K., Pati, S.On algebraic connectivity of graphs with at most two points of articulation in each block. Linear Multilinear Algebra, 60 ( 2012 ), 415–432. Google Scholar
Web15 de abr. de 2024 · The research about ABC spectral radius (largest eigenvalue of ABC matrix) of graphs is rather active in recent years. In this paper, we characterize the … http://files.ele-math.com/abstracts/oam-17-05-abs.pdf
WebFor a k-uniform hypergraph G, the ABC eigenvalues of G are defined as the eigenvalues of its ABC tensor, and in particular, the ABC spectral radius of G is defined as the spectral radius of its ABC tensor, denoted by ρABC(G). That is, ρABC(G) = ρ(ABC(G)).
Web13 de jan. de 2024 · We first establish a lower bound on the size and spectral radius of a graph G to guarantee that G contains a ... Spectra of Graphs (Springer, New York, 2011).Google Scholar [4] Godsil, C. and Royle, G., Algebraic Graph Theory, Graduate Texts in ... ‘ On the distance spectral radius of unicyclic graphs with perfect ... simply church house of prayerWebSpectral Radius of Graphs provides a thorough overview of important results on the spectral radius of adjacency matrix of graphs that have appeared in the literature in the preceding ten years, most of them with proofs, and including some previously unpublished results of the author. rays and bostonWeb1 de jul. de 2024 · ABC spectral radius. Unicyclic graph. 1. Introduction. Let G be a simple graph with vertex set an edge set . For , we denote by the degree of v, and by the neighborhood of v in G. A graph G is called k -regular if every vertex of G has precisely k … rays and a\\u0027s stand thereWebON THE ABC SPECTRAL RADIUS OF CACTUS GRAPHS ZHIBINDU ANDBO ZHOU∗ Abstract. Let G be a graph with vertex set V(G). Denote by d u the degree of vertex u in … rays and canes chickenWebIn this paper, we determine the unicyclic graphs of order n 5 with the smallest and first four largest arithmetic-geometric spectral radii. 2 Lemmas We need the following lemmas. Lemma 2.1 [10] Let M ba a nonnegative matrix of order n. Let x be a positive column vector of dimension n, i.e. every entry of x is positive. ray sand channelWebAbstract. 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. In this paper, we extend the largest ordering of Aα -spectral radius among all complements of bicyclic and tricyclic graphs with n vertices, respectively. rays and canes menuWeb24 de mar. de 2024 · The largest absolute value of a graph's spectrum is known as its spectral radius . The spectrum of a graph may be computed in the Wolfram Language using Eigenvalues [ AdjacencyMatrix [ g ]]. Precomputed spectra for many named graphs can be obtained using GraphData [ graph , "Spectrum" ]. simply chunky yarn