Efficient coloring of a large spectrum of graphs

2002 ◽  
Author(s):  
D. Kirovski ◽  
M. Potkonjak
Keyword(s):  
Spectrum Of Graphs

scholarly journals On the distance spectrum of graphs

2013 ◽  
Vol 439 (6) ◽  
pp. 1662-1669 ◽  
Author(s):  
Huiqiu Lin ◽  
Yuan Hong ◽  
Jianfeng Wang ◽  
Jinlong Shu
Keyword(s):  
Distance Spectrum ◽  
Spectrum Of Graphs

scholarly journals Spectral Sufficient Conditions on Pancyclic Graphs

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Guidong Yu ◽  
Tao Yu ◽  
Xiangwei Xia ◽  
Huan Xu
Keyword(s):  
Spectral Radius ◽  
Spectral Theory ◽  
Sufficient Conditions ◽  
Laplacian Spectral Radius ◽  
Signless Laplacian Spectral Radius ◽  
Signless Laplacian ◽  
Np Complete ◽  
Pancyclic Graphs ◽  
Theory Of Graphs ◽  
Spectrum Of Graphs

A pancyclic graph of order n is a graph with cycles of all possible lengths from 3 to n . In fact, it is NP-complete that deciding whether a graph is pancyclic. Because the spectrum of graphs is convenient to be calculated, in this study, we try to use the spectral theory of graphs to study this problem and give some sufficient conditions for a graph to be pancyclic in terms of the spectral radius and the signless Laplacian spectral radius of the graph.

scholarly journals On the Non-Adaptive Zero-Error Capacity of the Discrete Memoryless Two-Way Channel

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1518
Author(s):  
Yujie Gu ◽  
Ofer Shayevitz
Keyword(s):  
Linear Programming ◽  
Linear Codes ◽  
Single Letter ◽  
Capacity Region ◽  
Probability Of Error ◽  
Asymptotic Spectrum ◽  
Point To Point ◽  
The One ◽  
Outer Bound ◽  
Spectrum Of Graphs

We study the problem of communicating over a discrete memoryless two-way channel using non-adaptive schemes, under a zero probability of error criterion. We derive single-letter inner and outer bounds for the zero-error capacity region, based on random coding, linear programming, linear codes, and the asymptotic spectrum of graphs. Among others, we provide a single-letter outer bound based on a combination of Shannon’s vanishing-error capacity region and a two-way analogue of the linear programming bound for point-to-point channels, which, in contrast to the one-way case, is generally better than both. Moreover, we establish an outer bound for the zero-error capacity region of a two-way channel via the asymptotic spectrum of graphs, and show that this bound can be achieved in certain cases.

scholarly journals Distance spectrum and energy of graphs with small diameter

2017 ◽  
Vol 11 (1) ◽  
pp. 108-122 ◽  
Author(s):  
Milica Andjelic ◽  
Tamara Koledin ◽  
Zoran Stanic
Keyword(s):  
Adjacency Matrix ◽  
Small Diameter ◽  
Distance Spectrum ◽  
Spectrum Of Graphs ◽  
Equienergetic Graphs

In this paper we express the distance spectrum of graphs with small diameter in terms of the eigenvalues of their adjacency matrix. We also compute the distance energy of particular types of graph and determine a sequence of infinite families of distance equienergetic graphs.

scholarly journals Effects on the distance Laplacian spectrum of graphs with clusters by adding edges

2019 ◽  
Vol 35 ◽  
pp. 511-523
Author(s):  
Roberto Díaz ◽  
Oscar Rojo
Keyword(s):  
Complete Graph ◽  
Connected Graph ◽  
Laplacian Spectrum ◽  
Laplacian Eigenvalue ◽  
Laplacian Eigenvalues ◽  
The Matrix ◽  
Spectrum Of Graphs

All graphs considered are simple and undirected. A cluster in a graph is a pair of vertex subsets (C, S), where C is a maximal set of cardinality |C| ≥ 2 of independent vertices sharing the same set S of |S| neighbors. Let G be a connected graph on n vertices with a cluster (C, S) and H be a graph of order |C|. Let G(H) be the connected graph obtained from G and H when the edges of H are added to the edges of G by identifying the vertices of H with the vertices in C. It is proved that G and G(H) have in common n −|C| + 1 distance Laplacian eigenvalues, and the matrix having these common eigenvalues is given, if H is the complete graph on |C| vertices then ∂ −|C| + 2 is a distance Laplacian eigenvalue of G(H) with multiplicity|C| − 1, where ∂ is the transmission in G of the vertices in C. Furthermore, it is shown that if G is a graph of diameter at least 3, then the distance Laplacian spectral radii of G and G(H) are equal, and if G is a graph of diameter 2, then conditions for the equality of these spectral radii are established. Finally, the results are extended to graphs with two or more disjoint clusters.

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