Ela Disjoint Unions of Complete Graphs Characterized by Their Laplacian Spectrum∗
نویسنده
چکیده
A disjoint union of complete graphs is in general not determined by its Laplacian spectrum. It is shown in this paper that if one only considers the family of graphs without isolated vertex, then a disjoint union of complete graphs is determined by its Laplacian spectrum within this family. Moreover, it is shown that the disjoint union of two complete graphs with a and b vertices, a b > 5 3 and b > 1 is determined by its Laplacian spectrum. A counter-example is given when a b = 5 3 .
منابع مشابه
THE SPECTRAL DETERMINATION OF THE MULTICONE GRAPHS Kw ▽ C WITH RESPECT TO THEIR SIGNLESS LAPLACIAN SPECTRA
The main aim of this study is to characterize new classes of multicone graphs which are determined by their signless Laplacian spectra. A multicone graph is defined to be the join of a clique and a regular graph. Let C and K w denote the Clebsch graph and a complete graph on w vertices, respectively. In this paper, we show that the multicone graphs K w ▽C are determined by their signless ...
متن کاملON NEW CLASSES OF MULTICONE GRAPHS DETERMINED BY THEIR SPECTRUMS
A multicone graph is defined to be join of a clique and a regular graph. A graph $ G $ is cospectral with graph $ H $ if their adjacency matrices have the same eigenvalues. A graph $ G $ is said to be determined by its spectrum or DS for short, if for any graph $ H $ with $ Spec(G)=Spec(H)$, we conclude that $ G $ is isomorphic to $ H $. In this paper, we present new classes of multicone graphs...
متن کاملNormalized laplacian spectrum of two new types of join graphs
Let $G$ be a graph without an isolated vertex, the normalized Laplacian matrix $tilde{mathcal{L}}(G)$ is defined as $tilde{mathcal{L}}(G)=mathcal{D}^{-frac{1}{2}}mathcal{L}(G)mathcal{D}^{-frac{1}{2}}$, where $mathcal{D}$ is a diagonal matrix whose entries are degree of vertices of $G$. The eigenvalues of $tilde{mathcal{L}}(G)$ are called as the normalized Laplacian eigenva...
متن کاملEla Extremal Laplacian-energy-like Invariant of Graphs with given Matching Number∗
Let G be a graph of order n with Laplacian spectrum μ1 ≥ μ2 ≥ · · · ≥ μn. The Laplacian-energy-like invariant of graph G, LEL for short, is defined as: LEL(G) = n−1 ∑ k=1 √ μk . In this note, the extremal (maximal and minimal) LEL among all the connected graphs with given matching number is determined. The corresponding extremal graphs are completely characterized with respect to LEL. Moreover ...
متن کاملEla the Signless Laplacian Spectral Radius of Bicyclic Graphs with a given Girth
Let B(n, g) be the class of bicyclic graphs on n vertices with girth g. In this paper, the graphs in B(n, g) with the largest signless Laplacian spectral radius are characterized.
متن کامل