New proofs of the uniqueness of extremal noneven digraphs.
New theorems for signless Laplacian eigenvalues
Nodal domain theorems and bipartite subgraphs.
Non-complete extended -sum of graphs, graph angles and star partitions.
Nonderogatory directed windmills.
Nonexistence of almost Moore digraphs of diameter three.
Non-isomorphic graphs with cospectral symmetric powers.
Nonsingular unicyclic mixed graphs with at most three eigenvalues greater than two
This paper determines all nonsingular unicyclic mixed graphs on at least nine vertices with at most three Laplacian eigenvalues greater than two.
Non-surjective linear transformations of tropical matrices preserving the cyclicity index
The cyclicity index of a matrix is the cyclicity index of its critical subgraph, namely, the subgraph of the adjacency graph which consists of all cycles of the maximal average weight. The cyclicity index of a graph is the least common multiple of the cyclicity indices of all its maximal strongly connected subgraphs, and the cyclicity index of a strongly connected graph is the least common divisor of the lengths of its (directed) cycles. In this paper we obtain the characterization of linear, possibly...
Nordhaus-gaddum-type relations for the energy and Laplacian energy of graphs
Note on a conjecture for the sum of signless Laplacian eigenvalues
For a simple graph on vertices and an integer with , denote by the sum of largest signless Laplacian eigenvalues of . It was conjectured that , where is the number of edges of . This conjecture has been proved to be true for all graphs when , and for trees, unicyclic graphs, bicyclic graphs and regular graphs (for all ). In this note, this conjecture is proved to be true for all graphs when , and for some new classes of graphs.
Note on deleting a vertex and weak interlacing of the Laplacian spectrum.
Note on Estrada and -Estrada indices of graphs
Note on Laplacian energy of graphs
Nouvelles approches de la propriété (T) de Kazhdan
Un groupe localement compact a la propriété (T) de Kazhdan si la -cohomologie de tout -module hilbertien est nulle. Cette propriété de rigidité de la théorie des représentations de a trouvé des applications qui vont de la théorie ergodique à la théorie des graphes. Pendant près de 30 ans, les seuls exemples connus de groupes avec la propriété (T), provenaient des groupes algébriques simples sur les corps locaux, ou de leurs réseaux. La situation a radicalement changé ces dernières années :...
Nullity of Graphs
Nullity of Graphs: An Updated Survey
On a bound on algebraic connectivity: the case of equality
In a recent paper the authors proposed a lower bound on , where , , is an eigenvalue of a transition matrix of an ergodic Markov chain. The bound, which involved the group inverse of , was derived from a more general bound, due to Bauer, Deutsch, and Stoer, on the eigenvalues of a stochastic matrix other than its constant row sum. Here we adapt the bound to give a lower bound on the algebraic connectivity of an undirected graph, but principally consider the case of equality in the bound when...
On a generalization of perfect -matching
The paper is concerned with the existence of non-negative or positive solutions to , where is the vertex-edge incidence matrix of an undirected graph. The paper gives necessary and sufficient conditions for the existence of such a solution.
On asymptotic stability of passive linear electrical networks