On the nullity of unicyclic graphs
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 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 … Websolved completely. Much attention is focused on graphs with few edges, e.g. trees, unicyclic graphs, bicyclic graphs. The nullity of a tree can be given in explicity form in terms of the matching number of the tree; see e.g. [5] and [11] for discussion on trees with maximum nullity. Tan and Liu [14] give the nullity set of unicyclic graphs of ...
On the nullity of unicyclic graphs
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Web6 de abr. de 2024 · The \(\alpha \)-spectral radius of a connected graph G is the spectral radius of \(A_\alpha \)-matrix of G.In this paper, we discuss the methods for comparing … http://files.ele-math.com/abstracts/oam-09-18-abs.pdf
WebLet 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 … 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 …
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. 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.
Web17 de ago. de 2016 · Here, by using Theorem 19.2.13, we compute the nullity of triangular benzenoid graph G[n], depicted in Fig. 19.4.The maximum matching of G[n] is depicted …
WebJ.-M. Guo et al. / Linear Algebra and its Applications 431 (2009) 1293–1301 1295 Fig. 1. Three graphs U∗ 1,U ∗ 2 and U ∗ 3 in Proposition 1.4, where n 1 and n2 2. Let Xn be the set of the unicyclic graphs with n vertices and with η(G) = 0, and let Yn be the set of unicyclic graphs with n vertices each of which is obtained from an arbitrary elementary unicyclic … how can a teacher uphold equity in educationWebThis 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 how many patronus options pottermoreWeb2040 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 … how can a teenager create a budgetWebLet 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 how can a text be cohesive but not coherentWeb1 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. … how can a team leader motivate team membersWeb1 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 … how can a teenager invest his moneyWebA 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 C_n with n=1 or 2 (mod 4) are graceful (Gallian 2024). The numbers of unicyclic graphs on n=1, 2, ... vertices … how can a teacher support a student