By nullity of a graph we mean that of its adjacency matrix We determine the possible size of a graph with zero nullity. For any possible size we also construct a graph with zero nullity.Firouzeh AshiafHamidreza BamdadMatchF. Ashraf,H. Bamdad.A note on graphs with zero nullity.MATCH ...
In this paper we show the expression of the nullity and nullity set of unicyclic graphs with vertices and girth , and characterize the unicyclic graphs with extremal nullity.doi:10.4236/am.2014.510156Shengbiao HuApplied MathematicsW. Zhu, T.-Z. Wu, S.-B. Hu, A note on the nullity of ...
Bounds of nullity for complex unit gain graphs 2024, Linear Algebra and Its Applications Show abstract On connected T-gain graphs with rank equal to girth 2024, Linear Algebra and Its Applications Show abstract On the nullity of cycle-spliced T-gain graphs 2025, Communications in Combinatorics and...
.Notethatswitchingequivalenceisarelationofequivalence, and two switching equivalent graphs have the same nullities. A signed graph Γ is balanced if and only if Γ = (G, σ) ∼ (G, +) (see [1]). So the results on the nullity for simple graphs still hold for ...
has been made on graphs that are not trees, with most of the progress in the last few years. The rank or minimum rank of a family of matrices associated with a graph has also played a role in various other problems, including: • singular graphs, nullity of the adjacency matrix; •...
The 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.Shengbiao HuDepartment of ...
The number of zero eigenvalues in the spectrum of the graph G is called its nullity and is denoted by η(G).In this paper,we determine the all extremal unicyclic graphs achieving the fifth upper bound n-6 and the sixth upperbound n-7.数学研究及应用...
Cancellation can occur for graphs with one or more zero eigenvalues. For a non-zero contribution to total transmission, this requires that the source connection vertex is not a node for every orbital of the non-bonding shell. Conditions for individual lead transmissions involve both source and ...
In this paper graphs G that satisfy the equality η ( G ) = | V ( G ) | − 2 m ( G ) + 2 c ( G ) are characterized.Ya-zhiSongXiao-qiuSongBit-ShunTamSDOSLinear Algebra & Its ApplicationsYazhi Song, Xiaoqiu Song, Bit-Shun Tam, A characterization of graphs G with nullity V...
The nullity of graph is the presence of zero as an eigenvalue in the spectrum of G. In this paper, we have established the results on nullity of $(P_{n}\\odot S_{m})$ where $S_{m}$ is smith graph and $\\odot$ is corona product. Moreover we have shown that nullity of $...