The degree diameter problem
WebDegree-Diameter Problem -- from Wolfram MathWorld Degree-Diameter Problem A -graph is a graph with maximum vertex degree and diameter at most . The order of a graph with … WebThe degree/diameter problem is to determine the largest possible order of d-regular graphs with diameter D for given d and D 2. This is a fundamental problem in graph theory [1, 4, …
The degree diameter problem
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WebMar 7, 2024 · The "Degree diameter problem" is a graph theory problem that comes up in the design of computer networks, particularly peer-to-peer software networks or "virtual networks" (such as multi-player online gaming) and parallel processing architectures using node-to-node links for inter-CPU data exchange (Beowulf clusters worked this way). WebThe Maximum Degree-and-Diameter-Bounded Subgraph problem (MaxDDBS) is a problem in graph theory . Given a connected host graph G, an upper bound for the degree d, and an upper bound for the diameter k, we look for the largest subgraph S of G with maximum degree at most d and diameter at most k.
WebFeb 19, 2013 · We study the degree-diameter problem for claw-free graphs and 2-regular hypergraphs. Let be the largest order of a claw-free graph of maximum degree Δ and diameter D.We show that , where , for any D and any even .So for claw-free graphs, the well-known Moore bound can be strengthened considerably. WebJul 16, 2013 · The degree-diameter problem asks for the maximum number of vertices in a graph with maximum degree $\Delta$ and diameter $k$. For fixed $k$, the answer is …
WebFeb 28, 2013 · We consider the bipartite version of the degree/diameter problem, namely, given natural numbers d ≥ 2 and D ≥ 2, find the maximum number N b (d, D) of vertices in a bipartite graph of maximum degree d and diameter D. In this context, the bipartite Moore bound M b (d, D) represents a general upper bound for N b (d, D). WebJun 30, 2024 · The Degree Diameter problem is a classic extremal problem in network design. In particular, the Degree Diameter problem for mixed graphs asks for the largest possible number of vertices in a mixed graph with maximum undirected degree , maximum directed out-degree and diameter .
WebAug 24, 2024 · Our main result is that, for any graph of maximum degree \varDelta with more than 1.5 \varDelta ^t edges, its line graph must have diameter larger than t. In the case where the graph contains no cycle of length 2t+1, we can improve the bound on the number of edges to one that is exact for t\in \ {1,2,3,4,6\}.
WebDec 1, 2014 · The University of Newcastle, Australia Abstract and Figures The degree diameter problem involves finding the largest graph (in terms of the number of vertices) … flannel nightshirt with hathttp://www.mrob.com/pub/math/ttl-problem.html can screaming damage your vocal cordsIn graph theory, the degree diameter problem is the problem of finding the largest possible graph G (in terms of the size of its vertex set V) of diameter k such that the largest degree of any of the vertices in G is at most d. The size of G is bounded above by the Moore bound; for 1 < k and 2 < d only the Petersen graph, the Hoffman-Singleton graph, and possibly one more graph (not yet proven to exist) of diameter k = 2 and degree d = 57 attain the Moore bound. In general, the large… can screaming hurt your throatWebThe problem with a lower bound on diameter is NP-hard, while the problem with an upper bound on diameter is solvable in polynomial time. ... When we have no degree/diameter constraints, since spanning trees form a base family of a matroid, the exchange property of the matroid bases ensures that there always exists a reconfiguration sequence ... flannel no route to hostWebMar 16, 2024 · The existence of a Moore graph with degree 57 and diameter 2 is still open. As there are very few Moore graphs, it is interesting to ask the following the so-called … flannel nightshirt with nightcapWebThe degree/diameter problem is to determine the largest possible order of d-regular graphs with diameter D for given d and D 2. This is a fundamental problem in graph theory [1, 4, 11, 19]. As a regular graph often models a network topology, which the degree of each node is limited due to some physical constraints, flannel north face sweatshirt womensWebMay 16, 2013 · The degree-diameter problem seeks to find the largest possible number of vertices in a graph having given diameter and given maximum degree. Very often the problem is studied for restricted families… Expand 1 PDF A revised Moore bound for mixed graphs D. Buset, M. E. Amiri, Grahame Erskine, Mirka Miller, Hebert Pérez-Rosés … can screech appear in greenhouse doors