Linear Sphericity Testing of 3-connected Single Source Digraphs
نویسندگان
چکیده
It has been proved that sphericity testing for digraphs is an NP-complete problem. Here, we investigate sphericity of 3connected single source digraphs. We provide a new combinatorial characterization of sphericity and give a linear time algorithm for sphericity testing. Our algorithm tests whether a 3-connected single source digraph with n vertices is spherical in O(n) time.
منابع مشابه
Linear Sphericity Testing of 3-Connected Single Source Digraphs
It has been proved that sphericity testing for digraphs is an NP-complete problem. Here, we investigate sphericity of 3-connected single source digraphs. We provide a new combinatorial characterization of sphericity and give a linear time algorithm for sphericity testing. Our algorithm tests whether a 3-connected single source digraph with $n$ vertices is spherical in $O(n)$ time.
متن کاملOn spectral radius of strongly connected digraphs
It is known that the directed cycle of order $n$ uniquely achieves the minimum spectral radius among all strongly connected digraphs of order $nge 3$. In this paper, among others, we determine the digraphs which achieve the second, the third and the fourth minimum spectral radii respectively among strongly connected digraphs of order $nge 4$.
متن کاملSufficient conditions on the zeroth-order general Randic index for maximally edge-connected digraphs
Let D be a digraph with vertex set V(D) .For vertex v V(D), the degree of v, denoted by d(v), is defined as the minimum value if its out-degree and its in-degree . Now let D be a digraph with minimum degree and edge-connectivity If is real number, then the zeroth-order general Randic index is defined by . A digraph is maximally edge-connected if . In this paper we present sufficient condi...
متن کاملApplications of multivariate modeling to neuroimaging group analysis: A comprehensive alternative to univariate general linear model
All neuroimaging packages can handle group analysis with t-tests or general linear modeling (GLM). However, they are quite hamstrung when there are multiple within-subject factors or when quantitative covariates are involved in the presence of a within-subject factor. In addition, sphericity is typically assumed for the variance-covariance structure when there are more than two levels in a with...
متن کاملOptimal Upward Planarity Testing of Single-Source Digraphs
A digraph is upward planar if it has a planar drawing such that all the edges are monotone with respect to the vertical direction. Testing upward planarity and constructing upward planar drawings is important for displaying hierarchical network structures, which frequently arise in software engineering, project management, and visual languages. In this paper we investigate upward planarity test...
متن کامل