Results 21 to 30 of about 48,244 (304)
Some Characteristics of the Prime Graph of Integer Modulo Groups
InPrime, 2023 The notion of the prime graph of a ring R was first introduced by Bhavanari, Kuncham, and Dasari in 2010. The prime graph of a ring R, denoted by PG(R) is a graph whose vertices are all elements of the ring, where two distinct vertices x and y are ...
Muklas Maulana +3 more
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Note: Sharp Upper and Lower Bounds on the Number of Spanning Trees in Cartesian Product of Graphs
Discussiones Mathematicae Graph Theory, 2013 Let G1 and G2 be simple graphs and let n1 = |V (G1)|, m1 = |E(G1)|, n2 = |V (G2)| and m2 = |E(G2)|. In this paper we derive sharp upper and lower bounds for the number of spanning trees τ in the Cartesian product G1 □G2 of G1 and G2. We show that: and .
Azarija Jernej
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Completely Independent Spanning Trees in (Partial) k-Trees
Discussiones Mathematicae Graph Theory, 2015 Two spanning trees T1 and T2 of a graph G are completely independent if, for any two vertices u and v, the paths from u to v in T1 and T2 are internally disjoint.
Matsushita Masayoshi +2 more
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Spanning trees with a bounded number of leaves [PDF]
Opuscula Mathematica, 2017 In 1998, H. Broersma and H. Tuinstra proved that: Given a connected graph \(G\) with \(n\geq 3\) vertices, if \(d(u)+d(v)\geq n-k+1\) for all non-adjacent vertices \(u\) and \(v\) of \(G\) (\(k\geq 1\)), then \(G\) has a spanning tree with at most \(k ...
Junqing Cai +3 more
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On Independent [1, 2]-Sets in Trees
Discussiones Mathematicae Graph Theory, 2018 An [1, k]-set S in a graph G is a dominating set such that every vertex not in S has at most k neighbors in it. If the additional requirement that the set must be independent is added, the existence of such sets is not guaranteed in every graph.
Aleid Sahar A. +2 more
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Intersection of random spanning trees in complex networks
Applied Network Science, 2023 In their previous work, the authors considered the concept of random spanning tree intersection of complex networks (London and Pluhár, in: Cherifi, Mantegna, Rocha, Cherifi, Micciche (eds) Complex networks and their applications XI, Springer, Cham, 2023)
András London, András Pluhár
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Spanning k-ended trees of 3-regular connected graphs
Electronic Journal of Graph Theory and Applications, 2017 A vertex of degree one is called an end-vertex and the set of end-vertices of G is denoted by End(G). For a positive integer k, a tree T be called k-ended tree if $|End(T)| \leq k$. In this paper, we obtain sufficient conditions for spanning k-trees of 3-
Hamed Ghasemian Zoeram, Daniel Yaqubi
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Chain-Constrained Spanning Trees [PDF]
Mathematical Programming, 2013 We consider the problem of finding a spanning tree satisfying a family of additional constraints. Several settings have been considered previously, the most famous being the problem of finding a spanning tree with degree constraints. Since the problem is hard, the goal is typically to find a spanning tree that violates the constraints as little as ...
Olver, Neil, Zenklusen, Rico
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Number of Spanning Trees of Cartesian and Composition Products of Graphs and Chebyshev Polynomials
IEEE Access, 2019 Enumerating all the spanning trees of a graph without duplication is one of the widely studied problems in electrical engineering and computer science literature.
S. N. Daoud
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Non-crossing trees revisited: cutting down and spanning subtrees [PDF]
Discrete Mathematics & Theoretical Computer Science, 2003 Here we consider two parameters for random non-crossing trees: $\textit{(i)}$ the number of random cuts to destroy a size-$n$ non-crossing tree and $\textit{(ii)}$ the spanning subtree-size of $p$ randomly chosen nodes in a size-$n$ non-crossing tree ...
Alois Panholzer
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