Bulletin of the International Mathematical Virtual Institute

407-415

Authors: Derya Dogan Durgan and Ferhan Nihan Altundag

A set D  V (G) of a graph G = (V;E) is a liar's dominating set if (1) for all v 2 V (G) jN[v] \ Dj  2 and (2) for every pair u; v 2 V (G)of distinct vertices, jN[u] [ N[v] \ Dj  3. In this paper, we consider the liar's domination number of some middle graphs. Every triple dominating set is a liar's dominating set and every liar's dominating set must be a double dominating set. So, the liar's dominating set lies between double dominating set and triple dominating set.

427--435

Authors: O. Nethaji, I. Rajasekaran and O. Ravi

In this paper, another generalized class of tau⋆ called mildly Ig-omega-closed sets is introduced and the notion of mildly Ig-omega-open sets in ideal topological spaces is introduced and studied. The relationships of mildly Ig-omega-closed sets with various other sets are investigated.

445-450

Authors: K. Angaleeswaria and V. Swaminathan

Let G be a finite simple undirected graph. G is said to be a well covered graph if every maximal independent set is a maximum independent set. A graph is weakly well covered if every non-maximal independent set is contained in a maximum independent set. In an earlier paper, some results on weakly well covered graphs are derived. In this paper, a study of weakly well covered nature of G [ H, G + H, G  H, GH, G  H is made when G and H are weakly well covered graphs.

465-472

Authors: Dusko Jojic

All dissections of a convex (mn + 2)-gons into (m + 2)-gons are facets of a simplicial complex. This complex is introduced by S. Fomin and A.V. Zelevinsky in [7]. We reprove the result of E. Tzanaki about shellability of such complex by finding a concrete shelling order. Also, we use this shelling order to find a combinatorial interpretation of h-vector and to describe the generating facets of these complexes.

479-489

Authors: Ganesan Thangaraj and Raja Palani

In this paper, the concepts of fuzzy sigma-boundary set, fuzzy co-sigma-boundary set, in fuzzy topological spaces are introduced and studied. By means of fuzzy sigma-boundary sets, the concept of fuzzy weakly Baire space is defined and several characterizations of fuzzy weakly Baire spaces are studied.

505-514

Authors: I. Kulrekha Mudartha, R. Sundareswaran and V. Swaminathan

Terasa W. Haynes et. al. [7], introduced the concept of irredundance in graphs. A subset S of V (G) is called an irredundant set of G if for every vertex u 2 S, pn[u; S] ̸= ϕ. The minimum (maximum)cardinality of a maximal irredundant set of G is called the irredundance number of G (upper irredundance number of G) and is denoted by ir(G)(IR(G)). A subset V (G) is called an ir-set if it is an irredundant set of G of cardinality ir(G). A vertex u 2 V (G) is called ir-good if u belongs to an ir-set of G. G is said to be ir-excellent if every vertex of G is ir-good. In this paper, a study of the excellent graphs with respect to irredundance is initiated.

527--538

Authors: G. Mohanraj and E. Prabu

In this paper, we redefine the concepts of (landa; mi)-fuzzy right [left] ideals of hemirings by using the notions of fuzzy sum and fuzzy product. And also the notions of (landa; mi)-fuzzy right [left] h-ideals of hemirings are redefined by fuzzy sum, fuzzy closure and fuzzy product. Further, using the notions of fuzzy h-sum and fuzzy h-product, we characterize (lamda; mi)-fuzzy right [left] h-ideals. In particular, we investigate (landa; mi)-fuzzy right [left] h-ideals by using fuzzy h-sum and fuzzy h-intrinsic product.

549-560

Authors: Seyed Masoud Aghayan, Ahmad Zireh and Ali Ebadian

In this paper, we obtain the existence and the uniqueness of common best proximity point theorems for non-self mappings between two subsets of a complex valued metric space satisfying certain contractive conditions. Our results supported by some examples.

573-580

Authors: A.P. Santhakumaran, P. Titus and K. Ganesamoorthy

For a connected graph G = (V,E) of order at least two, a total detour monophonic set of a graph G is a detour monophonic set S such that the subgraph induced by S has no isolated vertices. The minimum cardinality of a total detour monophonic set of G is the total detour monophonic number of G and is denoted by dmt(G). A subset T of a minimum total detour monophonic set S of G is a forcing total detour monophonic subset for S if S is the unique minimum total detour monophonic set containing T. A forcing total detour monophonic subset for S of minimum cardinality is a minimum forcing total detour monophonic subset of S. The forcing total detour monophonic number ftdm(S) in G is the cardinality of a minimum forcing total detour monophonic subset of S. The forcing total detour monophonic number of G is ftdm(G) = min{ftdm(S)}, where the minimum is taken over all minimum total detour monophonic sets S in G. We determine bounds for it and find the forcing total detour monophonic number of certain classes of graphs. It is shown that for every pair a, b of positive integers with 0 6 a < b and b > 2a+1, there exists a connected graph G such that ftdm(G) = a and dmt(G) = b.