Results 51 to 60 of about 1,168 (127)

A linear algorithm for obtaining the Laplacian eigenvalues of a cograph

Special Matrices
In this article, we give an O(n)O\left(n) time and space algorithm for obtaining the Laplacian eigenvalues of a cograph. This approach is more efficient as there is no need to directly compute the eigenvalues of Laplacian matrix related to this class of ...
Chen Guantao, Tura Fernando C.
doaj   +1 more source

Designing classes’ interfaces for neural network graph model

Труды Института системного программирования РАН, 2019
An approach to testing artificial neural networks is described. The model of neural network is based on graph theory, and operations that are used in theoretical works devoted to graphs, trees, paths, cycles, and circuits.
Yuri Leonidovich Karpov, Irina Anatolievna Volkova, Alexey Alexandrovich Vylitok, Leonid Evgenievich Karpov, Yuri Gennadievich Smetanin   +4 more
doaj   +1 more source

Proofs Without Syntax

, 2006
"[M]athematicians care no more for logic than logicians for mathematics." Augustus de Morgan, 1868. Proofs are traditionally syntactic, inductively generated objects.
Hughes, Dominic
core   +4 more sources

On a Variant of the Minimum Path Cover Problem in Acyclic Digraphs: Computational Complexity Results and Exact Method

Networks, Volume 86, Issue 3, Page 325-357, October 2025.
ABSTRACT The Minimum Path Cover (MPC) problem consists of finding a minimum‐cardinality set of node‐disjoint paths that cover all nodes in a given graph. We explore a variant of the MPC problem on directed acyclic graphs (DAGs) where, given a subset of arcs, each path within the MPC should contain at least one arc from this subset.
Nour ElHouda Tellache, Roberto Baldacci
wiley   +1 more source

Some New Classes of Open Distance‐Pattern Uniform Graphs

International Journal of Combinatorics, Volume 2013, Issue 1, 2013., 2013
Given an arbitrary nonempty subset M of vertices in a graph G = (V, E), each vertex u in G is associated with the set fMo(u)={d(u,v) : v∈M, u≠v} and called its open M‐distance‐pattern. The graph G is called open distance‐pattern uniform (odpu‐) graph if there exists a subset M of V(G) such that fMo(u)=fMo(v) for all u, v ∈ V(G), and M is called an open
Bibin K. Jose, Toufik Mansour
wiley   +1 more source

CCSMR: A Combinatorial Category Space-Based Model for Recommendation

IEEE Access, 2019
Various side information has been exploited in recommender systems to help users finding items they prefer to alleviate data sparsity. Because item category can be used to view the user's preference in a high-level scope and an item can have more than ...
Chunjing Xiao, Kewen Xia, Leilei Sun, Cong Xie, Yuxiang Zhang   +4 more
doaj   +1 more source

Exact and Heuristic Solution Approaches for the Cluster Deletion Problem on General Graphs

Networks, Volume 85, Issue 4, Page 351-367, June 2025.
ABSTRACT A cluster graph is a disjoint union of cliques, obtained by clustering the nodes of a given network and then removing the edges between nodes assigned to different clusters. The Cluster Deletion problem asks for the smallest subset of edges to be removed from a network in order to produce a cluster graph, which is equivalent to determining the
Giuseppe Ambrosio, Raffaele Cerulli, Domenico Serra, Carmine Sorgente, Ugo Vaccaro   +4 more
wiley   +1 more source

On the Spectrum of Threshold Graphs

International Scholarly Research Notices, Volume 2011, Issue 1, 2011., 2011
The antiregular connected graph on r vertices is defined as the connected graph whose vertex degrees take the values of r − 1 distinct positive integers. We explore the spectrum of its adjacency matrix and show common properties with those of connected threshold graphs, having an equitable partition with a minimal number r of parts.
Irene Sciriha, Stephanie Farrugia, F. Ergun, P. Feinsilver, Y. Hou, S. Y. Song, N. I. Trinajstić   +6 more
wiley   +1 more source

Data Reduction for Graph Coloring Problems

, 2013
This paper studies the kernelization complexity of graph coloring problems with respect to certain structural parameterizations of the input instances. We are interested in how well polynomial-time data reduction can provably shrink instances of coloring
Bart M.P. Jansen, Bodlaender, Bodlaender, Bodlaender, Bodlaender, Bodlaender, Brandstädt, Bruce, Cai, Chor, Dell, Downey, Fellows, Fellows, Fiala, Fomin, Fomin, Fortnow, Garey, Guo, Hoàng, Jansen, Knuth, Kobler, Kratochvíl, Lokshtanov, Marx, Marx, Stefan Kratsch, Tuza, Yap   +30 more
core   +1 more source

The Rank of a Cograph

The Electronic Journal of Combinatorics, 2003
The rank of the adjacency matrix of a graph is bounded above by the number of distinct non-zero rows of that matrix. In general, the rank is lower than this number because there may be some non-trivial linear combination of the rows equal to zero. We show the somewhat surprising result that this never occurs for the class of cographs.
openaire   +2 more sources