A graph G = (V (G), E(G)) admits an H -covering if every edge in E belongs to a subgraph of G isomorphic to H . A graph G admitting an H -covering is called (a, d) -H -antimagic if there is a bijection f : V (G) ∪ E(G) → {1, 2, . . . , |V (G)| + |E(G)|} such that, for all subgraphs H ′ of G isomorphic to H , the H -weights, wtf (H ′) = ∑ v∈V (H′) f(v)+ ∑ e∈E(H′) f(e), constitute an arithmetic p...

A simple graph G = (V,E) admits an H-covering if every edge in E belongs at least to one subgraph of G isomorphic to a given graph H . Then the graph G admitting an H-covering is (a, d)-H-antimagic if there exists a bijection f : V ∪ E → {1, 2, . . . , |V | + |E|} such that, for all subgraphs H ′ of G isomorphic to H , the H ′-weights, wtf(H ′) = ∑ v∈V (H′) f(v) + ∑ e∈E(H′) f(e), form an arithm...

For given positive integers u and v with u ≡ v ≡ 0 (mod 6), let IRC(u; v) denote an incomplete resolvable minimum covering of pairs by triples of order u having a hole of size v. It is proved in this paper that there exists such an IRC(u; v) if and only if u¿ 3v. c © 2003 Elsevier B.V. All rights reserved.

The study of “covering lemmas” started with Jensen [DeJe] who proved in 1974–5 that in the absence of 0 there is a certain degree of resemblance between V and L. More precisely, if 0 does not exist then for every set of ordinals X there exists a set of ordinals Y ∈ L such that X ⊆ Y and V 2 |Y | = max{|X|,א1}. There is no hope of covering countable sets by countable ones in general, because doi...

In this paper we give a 2-generator 2-relation presentation for the group SL(2,121). This proves that SL(2,121), the covering group of PSL(2,121), is efficient

Given a vector space V and a non-singular quadratic form Q on V , the orthogonal group O(Q) is the subgroup of GL(V ) that preserves Q. The special orthogonal group SO(Q) is given by O(Q) ∩ SL(V ). If Q is the standard inner product on R then SO(Q) is denoted SO(n). This is a connected, compact Lie group. For n > 2, the group is semi-simple. In the case that n is odd, SO(n) corresponds to the D...

Sequential processes can encounter faults as a result of improper ordering of subsets of the events. In order to reveal faults caused by the relative ordering of t or fewer of v events, for some fixed t, a test suite must provide tests so that every ordering of every set of t or fewer events is exercised. Such a test suite is equivalent to a sequence covering array, a set of permutations on v e...