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In this paper, we define and characterize the f-graphs. Also, we give a construction of f-graphs and importantly we show that the f-graphs obtained from this construction are Cohen–Macaulay.

The notion of [Formula: see text]-ideal was introduced in [G. Q. Abbasi, S. Ahmad, I. Anwar and W. A. Baig, [Formula: see text]-Ideals of degree 2, Algebra Colloq. 19(1) (2012) 921–926] in 2012 and has been studied in many papers after that. In this paper, we have studied those graphs whose Stanley–Reisner ideals turn out to be [Formula: see text]-ideals. We give a characterization and construction of these graphs and show that, unlike [Formula: see text]-graphs, these graphs are always connected. We have also discussed when these graphs are complete bipartite graphs. Moreover, we classify those graphs for which both the facet ideal (the edge ideal) and the Stanley–Resiner ideal, are [Formula: see text]-ideals.

In this paper, we introduce the concept of [Formula: see text]-simplicial complexes by generalizing the term of [Formula: see text]-graphs (introduced in [H. Mahmood, I. Anwar and M. K. Zafar, Construction of Cohen–Macaualy [Formula: see text]-graphs, J. Algebra Appl. 13(6) (2014) 1450012]). In particular, we discuss the problem of connectedness of pure [Formula: see text]-simplicial complexes. Moreover, we give a complete characterization of connected and disconnected [Formula: see text]-graphs and give a classification of all the disconnected [Formula: see text]-graphs.

Abstract The self-mappings satisfying implicit relations were introduced in a previous study [Popa, Fixed point theorems for implicit contractive mappings, Stud. Cerc. St. Ser. Mat. Univ. Bacău 7 (1997), 129–133]. In this study, we introduce self-operators satisfying an ordered implicit relation and hence obtain their fixed points in the cone metric space under some additional conditions. We obtain a homotopy result as an application.

Let I be an ideal of a numerical semigroup Λ. We define an undirected graph GIΛ with vertex set vi:i∈Λ∖I∗=Λ∖I−0 and edge set vivj⟺i+j∈I. The aim of this article is to discuss the connectedness, girth, completeness, and some other related properties of the graph GIΛ.

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Communicated by B. BuchbergerIn this article we characterize the classification of uni-modal parametric plane curve singularities given by Ishikawa and Janeczko, in terms of invariants. On the basis of this characterization we present an algorithm to classify the uni-modal parametric plane 1750039-1 J. Algebra Appl. Downloaded from www.worldscientific.com by MCMASTER UNIVERSITY on 06/26/16. For personal use only. M. A. Binyamin et al.curve singularities and also give its implementation in computer algebra system SIN-GULAR.