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Kernels and Regularization on Graphs
Lecture Notes in Computer Science, 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
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Regular factors of regular graphs
Journal of Graph Theory, 1985AbstractGiven r ⩾ 3 and 1 ⩽ λ ⩽ r, we determine all values of k for which every r‐regular graph with edge‐connectivity λ has a k‐factor.
Béla Bollobás +2 more
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Journal of Graph Theory, 2017
AbstractA graph is called equimatchable if all of its maximal matchings have the same size. Kawarabayashi, Plummer, and Saito showed that the only connected equimatchable 3‐regular graphs are K4 and K3, 3. We extend this result by showing that for an odd positive integer r, if G is a connected equimatchable r‐regular graph, then .
Saieed Akbari +3 more
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AbstractA graph is called equimatchable if all of its maximal matchings have the same size. Kawarabayashi, Plummer, and Saito showed that the only connected equimatchable 3‐regular graphs are K4 and K3, 3. We extend this result by showing that for an odd positive integer r, if G is a connected equimatchable r‐regular graph, then .
Saieed Akbari +3 more
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Regular Graphs, Eigenvalues and Regular Factors
Journal of Graph Theory, 2011AbstractIn this article, we obtain a sufficient condition for the existence of regular factors in a regular graph in terms of its third largest eigenvalue. We also determine all values of k such that every r‐regular graph with the third largest eigenvalue at most has a k‐factor.
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Journal of Intelligent & Fuzzy Systems, 2016
A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, some properties of an edge regular vague graph are given.
Rajab Ali Borzooei +3 more
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A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, some properties of an edge regular vague graph are given.
Rajab Ali Borzooei +3 more
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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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Robust Multi-Label Feature Selection With Dual-Graph Regularization
Knowledge-Based Systems, 2020Wanfu Gao, Yonghao Li
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