5,316 research outputs found
Convolutional Graph-Tensor Net for Graph Data Completion
Graph data completion is a fundamentally important issue as data generally
has a graph structure, e.g., social networks, recommendation systems, and the
Internet of Things. We consider a graph where each node has a data matrix,
represented as a \textit{graph-tensor} by stacking the data matrices in the
third dimension. In this paper, we propose a \textit{Convolutional Graph-Tensor
Net} (\textit{Conv GT-Net}) for the graph data completion problem, which uses
deep neural networks to learn the general transform of graph-tensors. The
experimental results on the ego-Facebook data sets show that the proposed
\textit{Conv GT-Net} achieves significant improvements on both completion
accuracy (50\% higher) and completion speed (3.6x 8.1x faster) over the
existing algorithms
The spectral radius of minor free graphs
In this paper, we present a sharp upper bound for the spectral radius of an
-vertex graph without -minor for sufficient large , where is
obtained from the complete graph by deleting disjointed paths.
Furthermore, the graphs which achieved the sharp bound are characterized. This
result may be regarded to be an extended revision of the number of edges in an
-vertex graph without -minor.Comment: 18 pages, 1 figur
The signless Laplacian spectral radius of graphs without trees
Let be the signless Laplacian matrix of a simple graph of
order , where and are the degree diagonal matrix and the
adjacency matrix of , respectively. In this paper, we present a sharp upper
bound for the signless spectral radius of without any tree and characterize
all extremal graphs which attain the upper bound, which may be regarded as a
spectral extremal version for the famous Erd\H{o}s-S\'{o}s conjecture.Comment: 12 page
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