On the nullity of unicyclic graphs

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Web2040 H.-H. Li et al. / Linear Algebra and its Applications 437 (2012) 2038–2055 attaining the bounds n −2 and n −3, respectively.For the class of graphs with pendent vertices, Li [20] determined the extremal graphs which achieve the third and fourth upper bounds n − 4 and n − 5, respectively. Tan and Liu [28] studied the nullity and singularity of the unicyclic … Web1 de out. de 2008 · The nullity of a graph is the multiplicity of the eigenvalue zero in its spectrum. In this paper, we obtain the nullity set of bicyclic graphs of order n, and …

Characterizing Graphs with Nullity n-4 - Academia.edu

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 … Webthe unicyclic graphs with nullity n 6 and n 7. Li and Chang [10] gave the nullity set of three kinds of bicyclic graphs, and characterized two kinds of bicyclic graphs with nullity n 6. More results on the nullity of special classes of simple graphs can be found in the papers [11–19]. In this paper, we discuss the nullity of the signed graphs. grade 8 third term sinhala past papers

A Note on the Nullity of Unicyclic Graphs - Semantic Scholar

Web10 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 WebThe nullity of a graph is the multiplicity of the eigenvalue zero in its spectrum. In this paper we show the expression of the nullity and nullity set of unicyclic graphs with n vertices and girth r, and characterize the unicyclic graphs with extremal nullity. Web1 de jan. de 2014 · A Note on the Nullity of Unicyclic Graphs Authors: Shengbiao Hu Discover the world's research Join for free Public Full-text Available via license: CC BY … grade 8 third quarter summative test

On the nullity of the line graph of unicyclic graph with depth one

Linear Algebra and its Applications - CORE

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 … 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 chilterns councilWeb19 de jan. de 2024 · There has been significant work on the nullity of undirected graphs like trees [6, 8, 10], unicyclic graphs [12, 16], and bicyclic graphs [3, 5, 23]. It is well-known that a tree is nonsingular if and only if it has a perfect matching. chilterns circular walks

"WebLinear Algebra, Linear Models, Matrices and Graphs, Nonnegative Matrices , Graphs and Matrices in Graph Theory, Network Theory and Applications Expertise related to UN Sustainable Development Goals In 2015, UN member states agreed to 17 global Sustainable Development Goals (SDGs) to end poverty, protect the planet and ensure … " - On the nullity of unicyclic graphs

On the nullity of unicyclic graphs

On the Nullity of Bipartite Graphs SpringerLink

Web23 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 … 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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Web1 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 … Web2 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:

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 … Web22 de nov. de 2024 · 2.3 Unicyclic, Bicyclic, and Tricyclic Graphs. A unicyclic graph is a simple connected graph that has equal number of vertices and edges (contains a unique cycle). Let \(\mathcal {U}_{n}\) denote the set of all unicyclic graphs of order n. In , the nullity set as well as a characterization of unicyclic graphs with extremal nullity was …

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. … Web21 de nov. de 2024 · Gutman, I. and Borovćanin, B., ‘ Nullity of graphs: an updated survey ’, in: Selected Topics on Applications of Graph Spectra (eds. Cvetkovi ... ‘ On the nullity of the line graph of unicyclic graph with depth one ’, Linear Algebra Appl. 437 (2012) ...

WebThe 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 characterize the unicyclic … grade 8 third term test papers mathsWeb1 de jan. de 2012 · 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 Ck and Lk the set of all connected … chilterns council taxWeb15 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 … chiltern school staffWeb11 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. grade 8 third term test papers englishWebLet 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 nullity algorithm of tree and unicyclic graph. At the same time, to prove two algorithms are efficient. Keywords. Tree; Unicyclic Graph; Nullity Algorithm chilterns country lifestyleWeb1 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 … grade 8 third term test papers historyWeb1 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…. grade 8 third term papers 2022