Discrete Mathematics

The notion of --closed set was introduced and studied by R. Devi, V. Kokilavani and P. Basker [2]. In this paper, we introduce the concept of a -sets and studied the associated separation axioms.

The eccentric dominating graph EDmGabc(G) of a graph G is obtained from G with vertex set V? = V ? S, where V = V(G) and S is the set of all ?ed-sets of G. Two elements in V? are said to satisfy property ‘a’ if u, v ? V and are adjacent in G. Two elements in V? are said to satisfy property ‘b’ if u = D1, v = D2 ? S and have a common vertex. Two elements in V? are said to satisfy property ‘c’ if u ? V, v = D ? S such that u ? D. Two elements in V? are said to satisfy property ‘d’ if u, v ? V and there exists D ? S such that u, v ? D. A graph having vertex set V? and any two elements in V? are adjacent if and only if they satisfy any one of the property a, b, c is denoted by EDmGabc(G). In this paper EDmGabc(G) of some families of graphs and some basic properties of EDmGabc(G) are studied. Also, we have discussed the eccentricity properties of EDmGabc(G), and we have characterized graphs G for which EDmGabc(G) is complete or a tree.

A digraph D is a pair (V, A), where V is a non-empty set whose elements are called the vertices and A is the subset of the set of ordered pairs of distinct elements of V. The elements of A are called the arcs of D. A vertex v is a boundary vertex of u if d(u, w) ? d(u, v) for all w ? N(v). The boundary digraph BD(G) of a graph(digraph) G is the digraph that has the same vertex set as G and an arc from u to v exists in BD(G) if and only if v is a boundary vertex of u in G. The boundary neighbor digraph BND(G) of a graph G is the graph that has the same vertex set as G and a directed edge (arc) from u to v exists in BND(G) if and only if v is a boundary neighbor of u in G.

Linear complexity is a vital complexity measure and pseudorandom sequences with good correlation properties, large linear complexity, and balance statistics are widely used in modern communication and cryptology. This paper study the linear complexity of an inverse paths of a binary de Bruijn cycle by presenting set of pseudorandom binary sequences from de Bruijn graphs. And, it is shown that such sequences have large linear complexity.

In this paper we compute first and second neighborhood with respect to vertices and edges for some special graphs , and we discussed its algorithm.

A neighborhood set of an M-strong fuzzy graph is said to be independent neighborhood set if S is independent. is said to be perfect neighborhood set if all , the full fuzzy sub graphs and are edge disjoint. Also is said to be connected neighborhood set if full fuzzy sub graph is connected. The minimum scalar cardinality taken over all independent neighborhood set (perfect neighborhood set and connected neighborhood set) is called independent neighborhood number (perfect neighborhood number and connected neighborhood number). In this paper, these numbers are determined for various known fuzzy graphs and its relationship with some other known parameters of G is investigated.

For any graph G=( V,E ), the semitotal block graph T_b (G)=H, whose set of vertices is the union of the set of vertices and blocks of G and in which two vertices are adjacent if and only if the corresponding vertices of G are adjacent or the corresponding members are incident in G. For any two adjacent vertices u and v we say that u strongly dominates v if deg?(u)?deg?(v). A dominating set D of a graph H is a strong semitotal block dominating set of G if every vertex in V[T_b (G) ]-D is strongly dominated by at least one vertex in D. Strong semitotal block domination number ?_Stb (G) of G is the minimum cardinality of strong semitotal block dominating set of G. In this paper, we study graph theoretic properties of ?_Stb (G) and many bounds were obtain in terms of elements of G and its relationship with other domination parameters were found.

ABSTRACT Let be a fuzzy graph. Let be a subset of . is said to be a fuzzy metric basis of if for every pair of vertices , there exists a vertex such that The number of elements in is said to be fuzzy metric dimension (FMD) of and is denoted by . In this paper, we investigate the bounds for the fuzzy metric dimension of complete fuzzy graph and the bounds for total fuzzy star graph. Next we find the exact values of fuzzy metric dimension of Total graph of fuzzy path and fuzzy cycles and subdivision graph of fuzzy paths, fuzzy cycles and fuzzy star graph.

In this paper, we study 0 – modularity in the lattice of weak congruences. We are going to prove that Cw(L) is 0 – modular if and only if L is a chain.

This paper is about vertex transitive graphs and their domination related parameters. In particular we establish that all the vertices of a vertex transitive graph have the property that removal of any vertex from the graph either decreases the value of the parameter or does not change the value of the parameter.