JOURNAL OF INTERNATIONAL MATHEMATICAL VIRTUAL INSTITUTE

Counting the Average Size of Markov Graphs

Sergiy Kozerenko — 2017-02-02

We calculate the average size (i.e. number of arcs) of Markov
graphs for several classes of vertex maps on finite trees. These are include arbitrary maps, permutations, cyclic permutations and the so-called neighbourhood maps. In the latter case we obtain an explicit formula for the size of corresponding Markov graphs and then provide sharp bounds for it in terms of the underlying trees.

Laceability in the Modified Distance Graph of Grid Graphs

M. S. Annapoorna — 2017-02-02

A connected graph G is Hamiltonian-t-laceable if there exists in
it a Hamiltonian path between at least one pair of distinct vertices u and v with the property d(u; v) = t; 1 6 t 6 diamG. G is termed t-connected if it is Hamiltonian-t-laceable for all t. In this paper, we show that the modied distance graph of the grid graph Mgr(m; n) for n = m, 4 < m < 11 and for n = 2m, 2 < m < 8 is t-connected.

Normal Filters in Almost Distributive Lattices

Ramesh Sirisetti — 2017-02-02

In this paper we introduce normal lters and normlets in an almost
distributive lattice with dense elements and reinforce them in both algebraical and topological aspects.

On Banhatti and Zagreb Indices

I. Gutman — 2017-02-02

Let G = (V;E) be a connected graph. The Zagreb indices were in-
troduced as early as in 1972. They are dened as M1(G) =
Σ uv2E(G)[dG(u)+ dG(v)] and M2(G) = Σ uv2E(G) dG(u)dG(v), where dG(u) denotes the degree of a vertex u. The K Banhatti indices were introduced by Kulli in 2016. They are dened as B1(G) = Σ ue[dG(u) + dG(e)] and B2(G) = Σ ue dG(u)dG(e),
where ue means that the vertex u and edge e are incident and dG(e) denotes the degree of the edge e in G. These two typ es of indices are closely related. In this paper, we obtain some relations between them. We also provide lower and upper bounds for B1(G) and B2(G) of a connected graph in terms of Zagreb indices.

Fixed points of (fi,psi) - almost generalized weakly contractive maps with rational expressions in partially ordered metric spaces

Venkata Ravindranadh Babu Gutti — 2017-02-10

In this paper, we introduce a notion of (φ; )-almost generalized
weakly contractive maps involving rational type expressions in partially ordered metric spaces and prove the existence of xed points. These results generalize the results of Chandok, Choudhury and Metiya [16]. Also we provide examples in support of our results.

Fuzzy Prime Ideals in Ordered Г-Semirings

Marapureddy Murali Krishna Rao — 2017-02-13

We introduce the notion of ideal, prime ideal, fuzzy ideal, fuzzy
prime ideal of ordered Г -semiring and study their properties and relations between them. We characterize the prime ideals of ordered Г - semiring with respect to fuzzy ideals. And also characterize simple ordered Г - semiring with respect to fuzzy prime ideals of ordered We introduce the notion of ideal, prime ideal, fuzzy ideal, fuzzy

Decomposition of gω-continuity Idealization

K. Meena — 2017-04-13

In this paper we introduce the notions of g-I!-open sets, gp-I!-
open sets, gs-I!-open sets, g!t-I-sets, g! -I-sets and g!S-I-sets in ideal topological spaces and investigate some of their properties. Using these notions we obtain decompositions of g!-continuity.

Multi-valued fixed points results via rational type contractive conditions in complex valued metric spaces

Muhammad Sirajo Abdullahi — 2017-04-13

We establish some common xed point theorems for multi-valued
mappings in complex valued metric spaces satisfying rational type contractive conditions. Our results unify, extend and improve many recent results of the literature.