Spectra of unicyclic graphs

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August undefined, 2024

WebJul 1, 2024 · The ABC spectral radius of G, denoted by ν 1 ( G), is the largest eigenvalue of the ABC matrix of G. In this paper, we prove that for a unicyclic graph G of order n ≥ 4, 2 = ν 1 ( C n) ≤ ν 1 ( G) ≤ ν 1 ( S n + e), with equality if and only if G ≅ C n for the lower bound, and if and only if G ≅ S n + e for the upper bound. WebSearch within Zikai Tang's work. Search Search. Home; Zikai Tang

High-ordered spectral characterization of unicyclic graphs

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 (1984) conjectured that all unicyclic graphs except the cycle graph with … WebAug 28, 2024 · We prove that a class of unicyclic graphs with cospectral mates is DHS, and give two examples of infinitely many pairs of cospectral unicyclic graphs but with … paula patton music video

[2106.09238] On the spectral radius of unicyclic and bicyclic …

Web张海霞 ( 1.大连理工大学数学科学学院, 辽宁大连 116024;2.太原科技大学数学系, 山西太原 030024 ) . 按Laplace谱半径对一些偶单圈图的排序 WebThe spectrum of weighted graphs are often used to solve the problems in the design of networks and electronic circuits. In this article, we identify the (unique) weighted unicyclic … 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 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. paula patton in sacrifice

High-ordered spectral characterization of unicyclic graphs

The Aα -spectral radius of trees and unicyclic graphs with given …

WebJul 6, 2024 · We obtain some necessary conditions on the maximal-adjacency-spectrum unicyclic graphs in the set of unicyclic graphs with vertices and maximum degree and describe the structure of the maximal-adjacency-spectrum unicyclic graphs in the set. 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 ... paula patton movies 2021WebCharacterizing Graphs with Nullity n-4. Manjunatha Prasad Karantha. 2024, Match ... paula patton netflix series

"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 … " - Spectra of unicyclic graphs

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... 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 ...

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WebAs applications, we show that the greedy tree has the maximum Aα -spectral radius in G D when D is a tree degree sequence firstly. Furthermore, we determine that the greedy … 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 …

WebMar 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... WebFor integers n and Δ with 3 ≤ Δ ≤ n − 2, we prove that among the connected graphs on n vertices of given maximum degree Δ with at least one cycle, the graph U (n, Δ) uniquely maximizes the distance spectral radius, where U (n, Δ) is the graph obtained from the disjoint star on Δ vertices and path on n − Δ vertices by adding two ...

Webcospectral 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 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.

WebOct 10, 2006 · The spread s ( G) of a graph G is defined as s ( G ) = max i,j λ i − λ j , where the maximum is taken over all pairs of eigenvalues of G. Let U ( n, k) denote the set of all unicyclic graphs on n vertices with a maximum matching of cardinality k, and U * ( n, k) the set of triangle-free graphs in U ( n, k ).

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 … paula patton sacrifice full movieWebUnicyclic graphs are discussed in the context of graph orderings related to eigenvalues. Several theorems involving lexicographical ordering by spectral moments as well as the … paula patton son ageWebDec 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. paula patton son 2020WebIn 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 … paula patton sacrifice season 2WebMoreover, 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. paula patton photo galleryWebUnicyclic graphs are discussed in the context of graph orderings related to eigenvalues. Several theorems involving lexicographical ordering by spectral moments as well as the ordering by the largest eigenvalue are proved. Unicyclic graphs are discussed in the context of graph orderings related to … paula patton son todayWebJul 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 … paula pellegrini