Spanning Trees in a Class of Five Regular Small World Network
نویسندگان
چکیده
منابع مشابه
Spanning Trees in Regular Graphs
Let X be a regular graph with degree k 2 3 and order n. Then the number of spanning trees of X is where yk, ck and (3,,k(l/k) are positive constants, and p, is the number of equivalence classes of certain closed walks of length i in X. The value (k-l)k-l Ck = (k2_2k)"i/2)-l is shown to be the best possible in the sense that K(x~)"" +c^ for some increasing sequence X,, X2,.. . of regular graphs ...
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For a subset W of vertices of an undirected graph G, let S(W ) be the subgraph consisting of W , all edges incident to at least one vertex in W , and all vertices adjacent to at least one vertex in W . If S(W ) is a tree containing all the vertices of G, then we call it a spanning star tree of G. In this case W forms a weakly connected but strongly acyclic dominating set for G. We prove that fo...
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Let d > 3 be a fixed integer. We give an asympotic formula for the expected number of spanning trees in a uniformly random d-regular graph with n vertices. (The asymptotics are as n → ∞, restricted to even n if d is odd.) We also obtain the asymptotic distribution of the number of spanning trees in a uniformly random cubic graph, and conjecture that the corresponding result holds for arbitrary ...
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Let C ( G ) denote the number of spanning trees of a graph G . It is shown that there is a function ~ ( k ) that tends to zero as k tends to infinity such that for every connected, k-regular simple graph G on n vertices C ( G ) = {k[l u(G)]}", where 0 I u ( G ) I ~ ( k ) .
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ژورنال
عنوان ژورنال: Pure Mathematics
سال: 2017
ISSN: 2160-7583,2160-7605
DOI: 10.12677/pm.2017.75052