Results 241 to 250 of about 115,711 (260)
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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 .
Akbari, Saieed +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 .
Akbari, Saieed +3 more
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Regular two-graphs from strongly regular graphs
2022In this talk we will give a classification of strongly regular graphs with parameters (41, 20, 9, 10) that have a nontrivial automorphism. We will talk about the construction of regular two-graphs with 42 vertices from these strongly regular graphs and about the construction of regular two-graphs with 38 vertices.
Maksimović, Marija, Rukavina, Sanja
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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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1998
Abstract A graph is regular if all its vertices have the same degree; in particular, graphs that are regular of degree 3, 4, 5 and 6 are called, respectively, cubic, quartic, quintic and sextic. An example of each type is shown below. A regular graph is polyhedral if its vertices and edges correspond to the vertices and ...
Ronald C Read, Robin J Wilson
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Abstract A graph is regular if all its vertices have the same degree; in particular, graphs that are regular of degree 3, 4, 5 and 6 are called, respectively, cubic, quartic, quintic and sextic. An example of each type is shown below. A regular graph is polyhedral if its vertices and edges correspond to the vertices and ...
Ronald C Read, Robin J Wilson
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Journal of Graph Theory, 1988
AbstractA graph is pseudo‐median if for every triple u, v, w of vertices there exists either a unique vertex between each pair of them (if their mutual distances sum up to an even number) or a unique triangle whose edges lie between the three pairs of u, v, w, respectively (if the distance sum is odd).
Bandelt, Hans-Jürgen +1 more
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AbstractA graph is pseudo‐median if for every triple u, v, w of vertices there exists either a unique vertex between each pair of them (if their mutual distances sum up to an even number) or a unique triangle whose edges lie between the three pairs of u, v, w, respectively (if the distance sum is odd).
Bandelt, Hans-Jürgen +1 more
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Generating random regular graphs
Proceedings of the thirty-fifth ACM symposium on Theory of computing - STOC '03, 2003Random regular graphs play a central role in combinatorics and theoretical computer science. In this paper, we analyze a simple algorithm introduced by Steger and Wormald [10] and prove that it produces an asymptotically uniform random regular graph in a polynomial time.
Jeong Han Kim, Van H. Vu
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Journal of the London Mathematical Society, 1986
This paper completes the classification of cubic distance-regular graphs. We define the profile and period of certain cycles in such a graph, and obtain congruence conditions on the periods that help determine the feasible intersection arrays. It turns out that there are just 13 possible cases and in each case the array is realised by a unique graph.
Biggs, N.L. +2 more
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This paper completes the classification of cubic distance-regular graphs. We define the profile and period of certain cycles in such a graph, and obtain congruence conditions on the periods that help determine the feasible intersection arrays. It turns out that there are just 13 possible cases and in each case the array is realised by a unique graph.
Biggs, N.L. +2 more
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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.
Bollobás, Béla +2 more
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P4-decompositions of regular graphs
Journal of Graph Theory, 1999It is shown that every simple \(r\)-regular graph \(G\) admits a balanced \(P_4\)-decomposition if \(r \equiv 0\pmod 3\) and \(G\) has no cut-edge when \(r\) is odd. It is also shown that a connected 4-regular graph \(G\) admits a \(P_4\)-decomposition if and only if \(| E(G)| \equiv 0\pmod 3\) by characterizing graphs of maximum degree 4 that admit a ...
Heinrich, Katherine +2 more
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