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Category: Issue 4

Directed Circulant graphs and Binary Cyclic codes

GEORGE MATHEW
Department of Mathematics, BCM College Kottayam-686001, Kerala (India)
Email : gmathew5616x@gmail.com

ABSTRACT:

Various papers have been written on the theory of circulant graphs3,6,8,9,10. Also graphs with circulant adjacency matrices is discussed in7. Circulant graphs have important applications to the theory of designs and error correcting codes12. This paper is a study of relationship between circulant graphs and binary linear codes. It establishes a strong connection between directed circulant graphs and binary cyclic codes . Each binary cyclic code corresponds to an equivalence class of directed circulant graphs. Circulant graphs associated with combination of cyclic codes is also discussed.

KEYWORDS: Cayley graphs, circulant graphs, adjacency matrix, cyclic codes, generator polynomial, generator matrix.


Various papers have been written on the theory of circulant graphs3,6,8,9,10. Also graphs with circulant adjacency matrices is discussed in7. Circulant graphs have important applications to the theory of designs and error...

Smarandache-Alpha Level Subgroups

R. GOWRI1 and T. RAJESWARI 2
1Department of Mathematics, Government College for Women (Autonomous), Kumbakonam (India)
2 Research Scholar, Department of Mathematics, Government College for Women(Autonomous), Kumbakonam (India)
E-mail: rajeswari.mrt24@ gmail.com

ABSTRACT:

The concept of S - level subgroup of an S - fuzzy semigroup is defined and its characterizations are obtained. It is also discussed about S - fuzzy semigroups relative to a finite cyclic group.

KEYWORDS: S -Semigroup,fuzzy group,  -fuzzy set, S - fuzzy semigroup, level subgroups


Weakly Connected Closed Geodetic Numbers of the Corona and Composition of Some Graphs

RACHEL M. PATANGAN1, IMELDA S. ANIVERSARIO* and ROSALIO G. ARTES, JR.
Department of Mathematics and Statistics College of Science and Mathematics Mindanao State University-Iligan Institute of Technology 9200 Iligan City, Philippines
Email:-*imeldaaniversario@yahoo.com

ABSTRACT:

For two vertices u and v of a connected simple graph G, the closed interval IG[u,v] consists of u,v and all vertices lying in some u-v geodesic in G, while for SV(G), the set IG[S] is the union of all sets IG[u,v] for u,v S. In this paper, select vertices of G sequentially as follows: select avertex v1 and let S1 ={v1}. Select a vertex v2  v1 and let
S2={v1,v2}, then determine IG[S2]. If IG[S2]V(G), then successively select a vertex viIG[Si-1] and let Si={v1,v2,…,vi} for i=3,4,…,k. Then determine IG[Si].

A subset S of V (G) is called a weakly connected closed geodetic set of G if the selection of vertex vk in the given manner yields IG[Sk]= V(G), where Sk =S, and Sw is connected, where Sw=N[S], Ewwith Ew consists of edges uvE(G) such that uS or vS. The minimum cardinality of weakly connected closed geodetic set is called the weakly connected closed geodetic number wcgn(G) of G. In this paper, the weakly connected closed geodetic sets of the corona and composition of some graphs are characterized and the weakly connected closed geodetic numbers of these graphs are determined.

KEYWORDS: closed geodetic number of graph, weakly connected closed geodetic set, weakly connected closed geodetic number


Prime Labeling of Some Special Class of graphs

L. MEENAKSHI SUNDARAM* and A. NAGARAJAN
Department of Mathematics, V.O.Chidambaram College, Thoothukudi-628 008, Tamil Nadu (India)
Email:*lmsundar79@gmail.com

ABSTRACT:

Prime labeling originated with Entringer and was introduced by Tout, Dabboucy and Howalla5. A Graph G(V,E) is said to have a prime labeling if its vertices are labeled with distinct integers 1,2,3,…,V(G) such that for each edge xy, the labels assigned to x and y are relatively prime. A graph admits a prime labeling is called a prime graph. In this paper, we prove that Kn c+K2, (Kn c+K2)  K1, , Fm @ 2Pn, Cm @ 2Pn and are prime graphs

KEYWORDS: Prime Labeling, prime graphs