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Kernels and Regularization on Graphs
2003We introduce a family of kernels on graphs based on the notion of regularization operators. This generalizes in a natural way the notion of regularization and Greens functions, as commonly used for real valued functions, to graphs. It turns out that diffusion kernels can be found as a special case of our reasoning.
Alexander J. Smola, Risi Kondor
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Regularity of Congruential Graphs
2000The aim of this article is to make a link between the congruential systems investigated by Conway and the infinite graphs theory. We compare the graphs of congruential systems with a well known family of infinite graphs: the regular graphs of finite degree considered by Muller and Shupp, and by Courcelle.
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Ars Comb., 1996
A two-valued function \(f\) defined on the vertices of a graph \(G=(V,E)\), \(f:V\rightarrow \{-1,1\}\), is a signed dominating function if the sum of its function values over any closed neighborhood is at least one. It is a majority dominating function if this holds true for at least half of the neighborhoods.
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A two-valued function \(f\) defined on the vertices of a graph \(G=(V,E)\), \(f:V\rightarrow \{-1,1\}\), is a signed dominating function if the sum of its function values over any closed neighborhood is at least one. It is a majority dominating function if this holds true for at least half of the neighborhoods.
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Circumference of a regular graph
Journal of Graph Theory, 1989AbstractIt is proved that a 4‐connected, δ‐regular graph G either is Hamiltonian, or has at least 3δ + 1 vertices and contains a cycle of length at least min{4δ ‐ 4, 1/2 (|G| + 3δ ‐ 2)}. Examples supplied by B. Jackson and H.A. Jung show that min{4δ ‐ 4, 1/2(|G| + 3δ ‐ 2)} cannot be replaced by 4δ + 1.
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Decycling regular graphs [PDF]
If \(G\) is a graph and \(S\) is a set of vertices of \(G\) such that \(G-S\) is acyclic, then \(S\) is called decycling set of \(G\). The cardinality of the smallest decycling set of \(G\) is called the decycling number of \(G\) and it is denoted by \(\phi(G)\). It is shown, that if \({\mathbf d}\) is a fixed graphic degree sequence and \({\mathcal R}(
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Robust multi-label feature selection with dual-graph regularization
Knowledge-Based Systems, 2020Wanfu Gao, Jia Zhang
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Efficient and Robust MultiView Clustering With Anchor Graph Regularization
IEEE Transactions on Circuits and Systems for Video Technology, 2022Ben Yang, Xuetao Zhang, Zhiping Lin
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Superpixel-Based Graph Laplacian Regularization for Sparse Hyperspectral Unmixing
IEEE Geoscience and Remote Sensing Letters, 2022Taner Ince
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