On the nullity of unicyclic graphs

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 … 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.

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

WebHá 1 dia · The revised edge Szeged index of is defined as , where (resp., ) is the number of edges whose distance to vertex (resp., ) is smaller than the distance to vertex (resp., ), … 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 … tru haus shepherds https://clearchoicecontracting.net

On the nullity of unicyclic graphs - ScienceDirect

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 C_n with n=1 or 2 (mod 4) are graceful (Gallian 2024). The numbers of unicyclic graphs on n=1, 2, ... vertices … WebUN Sustainable Development Goals. In 2015, UN member states agreed to 17 global Sustainable Development Goals (SDGs) to end poverty, protect the planet and ensure prosperity for all. Our work contributes towards the following SDG(s): 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 … philip morris berlin news

On the $$\alpha $$ -spectral radius of unicyclic and bicyclic graphs ...

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On the nullity of unicyclic graphs

On the least eccentricity eigenvalue of graphs - ScienceDirect

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., … 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 …

On the nullity of unicyclic graphs

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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 … 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 …

WebHá 1 dia · Request PDF Vertex betweenness centrality of corona graphs and unicyclic graphs The idea of centrality measurements is quite appropriate for determining the … 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 …

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) ... 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 …

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 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 … philip morris biancheWebOn 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 , ... truhaven ranchphilip morris beogradWeb2040 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] … tru healing atlantaWeb23 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 nullity of bipartite graphs with no cycle of length a multiple of 4 as a subgraph. Among bipartite graphs on n vertices, the star has the greatest nullity (equal to n − 2). We … truhatch probioticsWebThe 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 … philip morris bestellungWeb2040 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 … tru haven insurance