On the nullity of unicyclic graphs

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August undefined, 2024

WebOn the nullity and the matching number of unicyclic graphs . × Close Log In. Log in with Facebook Log in with Google. or. Email. Password ... On the nullity and the matching number of unicyclic graphs. Weigen Yana. 2009, Linear Algebra and its Applications. Let G = (V(G), E(G)) be a simple graph with vertex set V (G) = {v 1 , v 2 , ... WebWe called graph G non-singular if adjacency matrix A (G) of G is non-singular. A connected graph with n vertices and n-1, n and n+1 edges are called the tree, the unicyclic graph …

On the permanental nullity and matching number of graphs

WebOther known results are, dimensions at least 3 were proven by Bong et al., for example, the 𝑚-shadow graph by Adawiyah et [12], for almost hypercube graphs by Alfarisi et al., al., … Web15 de out. de 2012 · In this paper, we shall give a complete characterization on the nullity of the line graph of unicyclic graph with depth one. Our main result is as follows. Theorem … shy swine who loves petunia

Unicyclic Graph -- from Wolfram MathWorld

WebThis has inspired a lot of researches on nullity of graph [8]-[14]. In this paper, by using three graph transformations which do not change the singularity, the non-singular trees, unicyclic graphs and bicyclic graphs are obtained. This method is different from previous. A connected graph of order n, the graph respectively with size nn−1, and Web15 de out. de 2012 · A connected graph with a unique cycle is called a unicyclic graph. A unicyclic graph with depth one may be thought of as being obtained from a cycle by … Web1 de out. de 2005 · The nullity of a graph is the multiplicity of the eigenvalue zero in its spectrum. In this paper, we obtain the nullity set of n-vertex unicyclic graphs, and … the peace of jesus verse

Centre for Advanced Research in Applied Mathematics and Statistics

WebLinear Algebra and its Applications. Volume 598, 1 August 2024, Pages 68-91. The strong spectral property for graphs Web1 de jan. de 2012 · Let G be a simple graph of order n and A (G) be its adjacency matrix. The nullity of a graph G, denoted by η (G), is the multiplicity of the eigenvalue zero in the spectrum of A (G).Denote by C k and L k the set of all connected graphs with k induced cycles and the set of line graphs of all graphs in C k, respectively.In 1998, Sciriha [I. … shysy cell lineWebWe called graph G non-singular if adjacency matrix A (G) of G is non-singular. A connected graph with n vertices and n-1, n and n+1 edges are called the tree, the unicyclic graph and the bicyclic graph. Respectively, as we all know, each connected bicyclic graph must contain ∞(a,s,b) or θ(p,l,q) as the induced subgraph. In this paper, by using three graph … shy-sy5y

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On the nullity of unicyclic graphs

Web11 de fev. de 2024 · A unicyclic graph G is of Type II if and only if every pendant tree \(G\lbrace {v}\rbrace \) is such that \(v\in {\text {Supp}(G\lbrace {v}\rbrace )}\). The following result computes the nullity of a unicyclic graph from the nullity of its pendant trees. Lemma 3.5 (Gong et al. 2010) Let G be a unicyclic graph and let C be its cycle. Web1 de jan. de 2024 · Note on the Unicyclic Graphs With the First Three Largest Wiener Indices by E. Glogić, Lj. Pavlović published in Kragujevac Journal of Mathematics. ... A Note on the Nullity of Unicyclic Graphs Applied Mathematics. 2014 English. The Largest Laplacian Spectral Radius of Unicyclic Graphs With Fixed Diameter

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WebOperators and Matrices Volume 9, Number 2 (2015), 311–324 doi:10.7153/oam-09-18 MORE ON THE MINIMUM SKEW–RANK OF GRAPHS HUI QU,GUIHAI YU ANDLIHUA FENG Abstract. The minimum (maximum) skew-rank of a simple graph G over real ﬁeld is the small- est (largest) possible rank among all skew-symmetric matrices over real ﬁeld … Web1 de nov. de 2011 · The nullity of a graph G, denoted by η (G), is the multiplicity of the eigenvalue zero in all eigenvalues of G. We investigate the maximal nullity among all …

WebA Note on the Nullity of Unicyclic Graphs Wei ZHU, Ting Zeng WU, Sheng Biao HU∗ Department of Mathematics, Qinghai Nationalities University, Qinghai 810007, P. R. China Abstract The number of zero eigenvalues in the spectrum of the graph G is called its nullity and is denoted by η(G). WebCharacterizing Graphs with Nullity n-4. Manjunatha Prasad Karantha. 2024, Match ...

Web1 de abr. de 2024 · A note on the multiplicities of the eigenvalues of a graph. C. Fonseca. Mathematics. 2005. Let A (G) be a Hermitian matrix whose graph is a given graph G. From the interlacing theorem, it is known that , where is the multiplicity of the eigenvalue θ of A (G). In this note we improve this…. 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 ordering by the largest eigenvalue are proved. An appendix contains a table of the 89 unicyclic graphs on eight vertices together with their spectra, spectral moments and …

Web1 de set. de 2009 · The nullity of unicyclic graphs For the sake of convenience, we will assume that G is a unicyclic graph with n vertices and the the cycle in G is denoted by …

Web1 de fev. de 2013 · In this paper we introduce the nullity of signed graphs, and give some results on the nullity of signed graphs with pendant trees. We characterize the … the peace of the lord - n. grant pfeiferWeb23 de mai. de 2009 · The nullity of a graph is the multiplicity of the eigenvalue zero in its spectrum. We obtain some lower bounds for the nullity of graphs and we then find the … shys vs shiesWeb2 de jul. de 2011 · The nullity of unicyclic signed graphs July 2011 DOI: arXiv Authors: Yi-Zheng Fan Anhui University Yue Wang Yi Wang Zhejiang University Request full-text … the peace of philocratesWeb2 de jul. de 2011 · In this paper we introduce the nullity of signed graphs, and give some results on the nullity of signed graphs with pendant trees. ... We characterize the unicyclic signed graphs of order n with nullity n-2; n-3; n-4; n-5 respectively. Subjects: Combinatorics (math.CO) MSC classes: 05C50: Cite as: shy synonym 8 lettersWebLet G be a graph with n vertices and q(G) be the maximum matching number of G. Let η(G) denote the nullity of G (the multiplicity of the eigenvalue zero of G). It is shown that the … the peace of parisWeb16 graph. 1) граф. 2) ... - nullity graph - odd graph - one-point graph - operator graph - order graph - orderable graph - ordinary graph - orientable graph - outer-embeddable graph - overlap graph ... - unicyclic graph - uniform graph - unilateral graph - unilaterally connected graph - unimodular graph shyt0wnWeb1 de dez. de 2010 · The nullity of a graph is defined as the multiplicity of the eigenvalue zero in the spectrum of the adjacency matrix of the graph. We investigate a class of … the peace of roaring river