# Turning All Lights Out

## Related Articles

- Bounds for joint spectral radii of a set of nonnegative matrices. Al’pin, Yu. // Mathematical Notes;Feb2010, Vol. 87 Issue 1/2, p12
Bounds for joint spectral radii of a set of nonnegative matrices are established by using the apparatus of idempotent algebra.

- Bounds for the Distance Estrada Index of Graphs. Altındağ, Ş. Burcu Bozkurt; Bozkurt, Durmuş // AIP Conference Proceedings;2015, Vol. 1648 Issue 1, p1
Let G be simple connected graph with n vertices. The distance eigenvalues Î¼1 â‰¥ Î¼2 â‰¥ ... â‰¥ Î¼n of G are the eigenvalues of its distance matrix D(G). The distance Estrada index of G is defined as DEE(G) = Î£i=1n eÎ¼i [14]. In this paper, we establish better lower...

- Quivers with potentials associated to triangulated surfaces. // Proceedings of the London Mathematical Society;May2009, Vol. 98 Issue 3, p797
We attempt to relate two recent developments: cluster algebras associated to triangulations of surfaces by Fominâ€“Shapiroâ€“Thurston, and quivers with potentials (QPs) and their mutations introduced by Derksenâ€“Weymanâ€“Zelevinsky. To each ideal triangulation of a bordered...

- The Least Eigenvalue of Graphs with Cut Edges. Wang, Yi; Fan, Yi-Zheng // Graphs & Combinatorics;Jul2012, Vol. 28 Issue 4, p555
In this paper we characterize the unique graph whose least eigenvalue attains the minimum among all connected graphs of fixed order and given number of cut edges.

- Seidel Integral Complete r-Partite Graphs. Wang, Ligong; Zhao, Guopeng; Li, Ke // Graphs & Combinatorics;Mar2014, Vol. 30 Issue 2, p479
A graph is S-integral (or Seidel integral) if the spectrum of its Seidel matrix consists entirely of integers. In this paper, we give a sufficient and necessary condition for complete r-partite graphs to be S-integral, from which we construct infinitely many new classes of S-integral graphs. We...

- The problem of reconstructing a quasihomogeneous string from its part. Sarkisyan, P. // Mathematical Notes;Jul2007, Vol. 82 Issue 1/2, p110
We consider quasihomogeneous strings with piecewise constant density and derive the quasihomogeneity condition. For a small number of string components, we present explicit formulas for reconstructing a string from its part. For an arbitrary number of string components, we construct a theory of...

- Investigating single-type structural elements of a component Petri net during component modeling and analysis of a complex system with parallelism. Lukyanova, E.; Derezaa, A. // Cybernetics & Systems Analysis;Nov2012, Vol. 48 Issue 6, p823
The process of modelling reactive distributed systems by a component Petri net (a CN-net) is considered. A mechanism for constructing composite components (places and transitions) of a CN-net is shown, and an analysis of a CN-net is demonstrated by the example of modelling the railroad traffic...

- THE MINIMUM SPECTRAL RADIUS OF SIGNLESS LAPLACIAN OF GRAPHS WITH A GIVEN CLIQUE NUMBER. LI SU; HONG-HAI LI; JING ZHANG // Discussiones Mathematicae: Graph Theory;2014, Vol. 34 Issue 1, p95
In this paper we observe that the minimal signless Laplacian spectral radius is obtained uniquely at the kite graph PKn-Ï‰,Ï‰ among all connected graphs with n vertices and clique number Ï‰. In addition, we show that the spectral radius Âµ of PKm,Ï‰ (m â‰¥ 1) satisfies 1/2...

- Harary's Theorem on Signed Graphs and Reversibility of Markov Chains. Al'pin, Yu. // Journal of Mathematical Sciences;Jun2014, Vol. 199 Issue 4, p375
A counterpart of the well-known Harary theorem on signed graphs is proved for digraphs over groups. This result is then used to derive a known theorem on the diagonal similarity of matrices and Kolmogorov's criterion of the reversibility of Markov chains.