The arrangement graph An;k is not only a generalization of star graph (nÿ k ˆ 1), but also more ̄exible. In this investigation, we elucidate the problem of embedding of multiple spanning trees in an arrangement graph with the objective of congestion-free. This result is to report how to exploit 2…nÿ k† edge disjoint spanning trees in an arrangement graph, where each congestion-free spanning tre...

We consider the problem of enumerating spanning trees on lattices. Closed-form expressions are obtained for the spanning tree generating function for a hypercubic lattice of size N1×N2×· · ·×Nd in d dimensions under free, periodic, and a combination of free and periodic boundary conditions. Results are also obtained for a simple quartic net embedded on two non-orientable surfaces, a Möbius stri...

A spanning tree of graph G is a spanning subgraph of G that is a tree. In this paper, we focus our attention on (n,m) graphs, where m = n, n + 1, n + 2, n+3 and n + 4. We also determine some coefficients of the Laplacian characteristic polynomial of fullerene graphs.

We prove the rather counterintuitive result that there exist finite transitive graphs H and integers k such Free Uniform Spanning Forest in direct product of k-regular tree has infinitely many trees almost surely. This shows number FUSF is not a quasi-isometry invariant. Moreover, we give two different Cayley same virtually free group one, but connected other, answering question Lyons Peres (Pr...

A graph is called 2K2-free if it does not contain two independent edges as an induced subgraph. Mou and Pasechnik conjectured that every 3 2 -tough 2K2-free graph with at least three vertices has a spanning trail with maximum degree at most 4. In this paper, we confirm this conjecture. We also provide examples for all t < 54 of t-tough graphs that do not have a spanning trail with maximum degre...

The source and target reliability in SAT network is de- fined as the flawless transmission from the source node to all the other nodes. In some references, the SAT pro- cess has been followed between all the node pairs but it is very time-consuming in today’s widespread networks and involves many costs. In this article, a method has been proposed to compare the reliability in complex networks b...

Let G be a 2-connected claw-free graph. We show that • if G is N1,1,4-free or N1,2,2-free or Z5-free or P8-free, respectively, then G has a spanning eulerian subgraph (i.e. a spanning connected even subgraph) or its closure is the line graph of a graph in a family of well-defined graphs, • if the minimum degree δ(G) ≥ 3 and G is N2,2,5-free or Z9-free, respectively, then G has a spanning euleri...

Given n red and n blue points in the plane and a planar straight line matching between the red and the blue points, the matching can be extended into a bipartite planar straight line spanning tree. That is, any red-blue planar matching can be completed into a crossing-free red-blue spanning tree. Such a tree can be constructed in O(n log n) time. keywords: geometric graph, spanning tree, color