We shall term a group G supersoluble if every homomorphic image H9*l of G contains a cyclic normal subgroup different from 1. Supersoluble groups with maximum condition, in particular finite supersoluble groups, have been investigated by various authors: Hirsch, Ore, Zappa and more recently Huppert and Wielandt. In the present note we want to establish the close connection between supersoluble ...

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 ...

A necessary and sufficient condition is given for a subshift presentation to have a continuous g-function. An invariant necessary and sufficient condition is formulated for a subshift to posses a presentation that has a continuous g-function.

We investigate valued fields which admit a valuation basis. Given a countable ordered abelian group G and a real closed, or algebraically closed field F , we give a sufficient condition for a valued subfield of the field of generalized power series F ((G)) to admit a K-valuation basis. We show that the field of rational functions F (G) and the field F (G) of power series in F ((G)) algebraic ov...

In this paper we proved that every g-Riesz basis for Hilbert space $H$ with respect to $K$ by adding a condition is a Riesz basis for Hilbert $B(K)$-module $B(H,K)$. This is an extension of [A. Askarizadeh, M. A. Dehghan, {em G-frames as special frames}, Turk. J. Math., 35, (2011) 1-11]. Also, we derived similar results for g-orthonormal and orthogonal bases. Some relationships between dual fra...

These notes show how to get rid of the idempotence condition (G = G;G) in (δ)-Size Change Termination. Both the “graph algorithm” of the original SCT paper [LJBA01] and the δSCT criterion of BenAmram [BA06] use some kind of idempotence on the potential cycles. This idempotence condition can be replaced by a more semantical condition on the cycles. The new condition is probably not easier to com...

A vertex subset X of a graph G is said to be cyclable in G if there is a cycle in G containing all vertices of X. Ore [6] showed that the vertex set of G with cardinality n ≥ 3 is cyclable (i.e. G is hamiltonian) if the degree sum of any pair of nonadjacent vertices in G is at least n. Shi [8] and Ota [7] respectively generalized Ore’s result by considering the cyclability of any vertex subset ...

Given a graph class G, it is natural to ask whether a given graph has a connected or a total dominating set inducing a graph in G and, if so, what is the minimal size of such a set. We give a sufficient condition on G for the intractability of this problem. This condition is fulfilled by a wide range of graph classes.

‎There is a flatness property of acts over monoids called Condition $(PWP)$ which‎, ‎so far‎, ‎has received‎ ‎much attention‎. ‎In this paper‎, ‎we introduce Condition GP-$(P)$‎, ‎which is a generalization of Condition $(PWP)$‎. ‎Firstly‎, ‎some  characterizations of monoids by Condition GP-$(P)$ of their‎ ‎(cyclic‎, ‎Rees factor) acts are given‎, ‎and many known results are generalized‎. ‎More...