62,429 research outputs found
Degree Associated Edge Reconstruction Number of Graphs with Regular Pruned Graph
An ecard of a graph is a subgraph formed by deleting an edge. A da-ecard specifies the degree of the deleted edge along with the ecard. The degree associated edge reconstruction number of a graph is the minimum number of da-ecards that uniquely determines The adversary degree associated edge reconstruction number of a graph is the minimum number such that every collection of da-ecards of uniquely determines The maximal subgraph without end vertices of a graph which is not a tree is the pruned graph of It is shown that of complete multipartite graphs and some connected graphs with regular pruned graph is or We also determine and of corona product of standard graphs
Degree Associated Reconstruction Parameters of Total Graphs
A card (ecard) of a graph G is a subgraph formed by deleting a vertex (an edge). A dacard (da-ecard) specifies the degree of the deleted vertex (edge) along with the card (ecard). The degree associated reconstruction number (degree associated edge reconstruction number ) of a graph G, drn(G) (dern(G)), is the minimum number of dacards (da-ecards) that uniquely determines G. In this paper, we investigate these two parameters for the total graph of certain standard graphs
Degree Associated Reconstruction Parameters of Total Graphs
A card (ecard) of a graph G is a subgraph formed by deleting a vertex (an edge). A dacard (da-ecard) specifies the degree of the deleted vertex (edge) along with the card (ecard). The degree associated reconstruction number (degree associated edge reconstruction number ) of a graph G, drn(G) (dern(G)), is the minimum number of dacards (da-ecards) that uniquely determines G. In this paper, we investigate these two parameters for the total graph of certain standard graphs
Local-set-based Graph Signal Reconstruction
Signal processing on graph is attracting more and more attentions. For a
graph signal in the low-frequency subspace, the missing data associated with
unsampled vertices can be reconstructed through the sampled data by exploiting
the smoothness of the graph signal. In this paper, the concept of local set is
introduced and two local-set-based iterative methods are proposed to
reconstruct bandlimited graph signal from sampled data. In each iteration, one
of the proposed methods reweights the sampled residuals for different vertices,
while the other propagates the sampled residuals in their respective local
sets. These algorithms are built on frame theory and the concept of local sets,
based on which several frames and contraction operators are proposed. We then
prove that the reconstruction methods converge to the original signal under
certain conditions and demonstrate the new methods lead to a significantly
faster convergence compared with the baseline method. Furthermore, the
correspondence between graph signal sampling and time-domain irregular sampling
is analyzed comprehensively, which may be helpful to future works on graph
signals. Computer simulations are conducted. The experimental results
demonstrate the effectiveness of the reconstruction methods in various sampling
geometries, imprecise priori knowledge of cutoff frequency, and noisy
scenarios.Comment: 28 pages, 9 figures, 6 tables, journal manuscrip
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