A k-tree is a tree with maximum degree at most k. In this paper, we give a degree sum condition for a graph to have a spanning k-tree in which specified vertices have degree less than k. We denote by σk(G) the minimum value of the degree sum of k independent vertices in a graph G. Let k ≥ 3 and s ≥ 0 be integers, and suppose G is a connected graph and σk(G) ≥ |V (G)|+s−1. Then for any s specifi...

For any simple connected graph $G=(V,E)$, a defensive alliance is a subset $S$ of $V$ satisfying the condition that every vertex $vin S$ has at most one more neighbour in $V-S$ than it has in $S$. The minimum cardinality of any defensive alliance in $G$ is called the alliance number of $G$, denoted $a(G)$. In this paper, we introduce a new type of alliance number called $k$-strong alliance numb...

DeTemple, D.W.. M.J. Dineen, J.M. Robertson and K.L. McAvaney, theory of partition graphs, Discrete Mathematics 113 (1993) 255-258. examples in the A partition graph is an intersection graph for a collection of subsets of a universal set S with the property that every maximal independent set of vertices corresponds to a partition of S. Two questions which arose in the study of partition graphs ...

Let G(m×n)  (m ≥ n) be a complex random matrix and W = G(m×n)(H)G(m×n) which is the complex Wishart matrix. Let λ1 > λ2 > …>λn > 0 and σ1 > σ2 > …>σn > 0 denote the eigenvalues of the W and singular values of G(m×n), respectively. The 2-norm condition number of G(m×n) is k2(G(m×n)) = √(λ1/λn) =σ1/σn. In this paper, the exact distribution of the condition number of the complex Wishart matrices i...

For a domain $G$ in the one-point compactification $\overline{\mathbb{R}}^n = \mathbb{R}^n \cup \{ \infty\}$ of $\mathbb{R}^n, n \ge 2$, we characterize completeness modulus metric $\mu_G$ terms potential-theoretic thickness condition $\partial G\,,$ Martio's $M$-condition. Next, prove that G$ is uniformly perfect if and only admits minorant M\"obius invariant metric. Several applications to qu...

Given a group G and a subgroup H, under what circumstances can we find a homomorphism φ : G −→ G', such that H is the kernel of φ? Clearly a necessary condition is that H is normal in G. Somewhat surprisingly this trivially necessary condition is also in fact sufficient. The idea is as follows. Given G and H there is an obvious map of sets, where H is the inverse image of a point. We just put X...

Let G be a locally compact group. The notion of "totally real" unitary representation of G is defined and investigated in §1. In particular, if K is a compact subgroup of G, it is shown that every closed G-invariant subspace of L2(G/K) is spanned by real-valued functions if, and only if, KgK=Kg~K for every geG. In §2 the coset space X=G/K is specialized to a Riemannian symmetric space, where th...

BACKGROUND Consensus on whether physical condition affects the risk of gravity-induced loss of consciousness (G-LOC) has not been reached, and most previous studies about the issue did not include well-experienced aviators. We compared the physical conditions of well-experienced young aviators according to the occurrence of G-LOC during human centrifuge training. METHODS Among 361 young male ...

A Garside group is a group admitting a finite lattice generating set D. Using techniques developed by Bestvina for Artin groups of finite type, we construct K(π, 1)s for Garside groups. This construction shows that the (co)homology of any Garside group G is easily computed given the lattice D, and there is a simple sufficient condition that implies G is a duality group. The universal covers of ...

A graph G is said to have a totally magic cordial labeling with constant C if there exists a mapping f : V (G) ∪ E(G) → {0, 1} such that f(a) + f(b) + f(ab) ≡ C (mod 2) for all ab ∈ E(G) and |nf (0) − nf (1)| ≤ 1, where nf (i) (i = 0, 1) is the sum of the number of vertices and edges with label i. In this paper, we give a necessary condition for an odd graph to be not totally magic cordial and ...