We investigate the properties of the spanning trees of various real-world and model networks. The spanning tree representing the communication kernel of the original network is determined by maximizing the total weight of the edges, whose weights are given by the edge betweenness centralities. We find that a scale-free tree and shortcuts organize a complex network. Especially, in ubiquitous sca...

We consider the problem of deciding whether or not a geometric graph has a crossing-free spanning tree. This problem is known to be NP-hard even for very restricted types of geometric graphs. In this paper, we present an O(n) time algorithm to solve this problem for the special case of geometric graphs that arise as visibility graphs of a finite set of n points between two monotone polygonal ob...

We propose an univesal scheme to design loop-free and superstabilizing protocols for constructing spanning trees optimizing any tree metrics (not only those that are isomorphic to a shortest path tree). Our scheme combines a novel super-stabilizing loop-free BFS with an existing self-stabilizing spanning tree that optimizes a given metric. The composition result preserves the best properties of...

a spanning tree of graph g is a spanning subgraph of g that is a tree. in this paper, we focusour attention on (n,m) graphs, where m = n, n + 1, n + 2 and n + 3. we also determine somecoefficients of the laplacian characteristic polynomial of fullerene graphs.

Free spans or suspended spans normally occur in subsea pipelines due to the irregularity of seabed and byscouring phenomena around the installed non-buried pipeline. The hydrodynamic around the pipeline canlead to a vibration of the pipeline.This kind of vibration may cause fatigue damage to the pipeline. In orderto study the hydrodynamic around the pipeline, calculating the natural frequency o...

Let τ(G) and τG(e) denote the number of spanning trees of a graph G and the number of spanning trees of G containing edge e of G, respectively. Ferrara, Gould, and Suffel asked if, for every rational 0 < p/q < 1 there existed a graph G with edge e ∈ E(G) such that τG(e)/τ(G) = p/q. In this note we provide constructions that show this is indeed the case. Moreover, we show this is true even if we...