On the nullity of unicyclic graphs
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: 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 nullity of unicyclic graphs
Did you know?
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 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. …
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] … 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 ...
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 … 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) ...
http://files.ele-math.com/abstracts/oam-09-18-abs.pdf
Web16 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 greenland\u0027s icy mountainsWeb1 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…. greenland\\u0027s militaryWeb23 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 … greenland\\u0027s lodge of spruce creekWebA 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 … fly fishing in delawareWebLet 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 … greenland\u0027s militaryWebThis 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 fly fishing in cold weatherWeb19 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. greenland\\u0027s national flower