Conditions for a totally positive completion in the case of a symmetrically placed cycle.
Johnson, Charles R., Kroschel, Brenda K. (2011)
ELA. The Electronic Journal of Linear Algebra [electronic only]
Sebastian M. Cioabă, Xiaofeng Gu (2016)
Czechoslovak Mathematical Journal
The eigenvalues of graphs are related to many of its combinatorial properties. In his fundamental work, Fiedler showed the close connections between the Laplacian eigenvalues and eigenvectors of a graph and its vertex-connectivity and edge-connectivity. We present some new results describing the connections between the spectrum of a regular graph and other combinatorial parameters such as its generalized connectivity, toughness, and the existence of spanning trees with bounded degree.
J. E. Boillat (1993)
Czechoslovak Mathematical Journal
C.D. Godsil, B.D. McKay (1982)
Aequationes mathematicae
Wang, Ligong, Hoede, Cornelis (2008)
The Electronic Journal of Combinatorics [electronic only]
Stephen J. Kirkland (1999)
Czechoslovak Mathematical Journal
A tree is classified as being type I provided that there are two or more Perron branches at its characteristic vertex. The question arises as to how one might construct such a tree in which the Perron branches at the characteristic vertex are not isomorphic. Motivated by an example of Grone and Merris, we produce a large class of such trees, and show how to construct others from them. We also investigate some of the properties of a subclass of these trees. Throughout, we exploit connections between...
D. Cvetković, P. Rowlinson, Z. Stanić, M. G. Yoon (2011)
Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques
Brouwer, A.E., Spence, E. (2009)
The Electronic Journal of Combinatorics [electronic only]
Dragoš Cvetković, Mirko Lepović (2005)
Publications de l'Institut Mathématique
Milica Anđelić, C. M. da Fonseca (2009)
Czechoslovak Mathematical Journal
We analyze the spectra of the cover matrix of a given poset. Some consequences on the multiplicities are provided.
Vandana P. Bhamre, Madhukar M. Pawar (2023)
Mathematica Bohemica
The concept of covering energy of a poset is known and its McClelland type bounds are available in the literature. In this paper, we establish formulas for the covering energy of a crown with elements and a fence with elements. A lower bound for the largest eigenvalue of a poset is established. Using this lower bound, we improve the McClelland type bounds for the covering energy for some special classes of posets.
Chung, Fan, Yau, S.-T. (1999)
The Electronic Journal of Combinatorics [electronic only]
Brasseur, Clara E., Grady, Ryan E., Prassidis, Stratos (2009)
The Electronic Journal of Combinatorics [electronic only]
Bernard Ycart (2007)
Annales de l’institut Fourier
If is the combinatorial Laplacian of a graph, converges to a matrix with identical coefficients. The speed of convergence is measured by the maximal entropy distance. When the graph is the sum of a large number of components, a cut-off phenomenon may occur: before some instant the distance to equilibrium tends to infinity; after that instant it tends to . A sufficient condition for cut-off is given, and the cut-off instant is expressed as a function of the gap and eigenvectors of components....
Grone, Robert, Merris, Russell (1988)
Portugaliae mathematica
Gopalapillai Indulal, Ivan Gutman (2009)
Kragujevac Journal of Mathematics
Sudhir R. Jog, Satish P. Hande, Ivan Gutman, S. Burcu Bozkurt (2012)
Kragujevac Journal of Mathematics
Yves Colin de Verdière (1999)
Annales de l'institut Fourier
On présente ici une approche directe et géométrique pour le calcul des déterminants d’opérateurs de type Schrödinger sur un graphe fini. Du calcul de l’intégrale de Fresnel associée, on déduit le déterminant. Le calcul des intégrales de Fresnel est grandement facilité par l’utilisation simultanée du théorème de Fubini et d’une version linéaire du calcul symbolique des opérateurs intégraux de Fourier. On obtient de façon directe une formule générale exprimant le déterminant en terme des conditions...
Loewy, Raphael (1985/1986)
Portugaliae mathematica
Kirkland, S., Olesky, D.D., van den Driessche, P. (2000)
ELA. The Electronic Journal of Linear Algebra [electronic only]