# Decomposition of various graphs in to sum divisor cordial graphs

Document Type : Primary Research paper

Authors

1 Research Scholar, PG and Research Department of Mathematics, Government Arts and Science College, Kangeyam, Tiruppur – 638 108, Tamil Nadu, India.

2 Assistant Professor, PG and Research Department of Mathematics, Government Arts and Science College, Kangeyam, Tiruppur – 638 108, Tamil Nadu, India.

Abstract

A sum divisor cordial labeling of a graph G with vertex set V is a bijection
f :V 1,2,3,...V(G) and the edge labeling : 0,1  f E is defined by   1  f uv , if 2
divides f (u)  f (v) and 0 otherwise. The function f is called a sum divisor cordial labeling
if (0)  (1) 1   f f
e e .That is the number of edges labeled with 0 and the number of edges
labeled with 1 differs by at most 1. A graph with a sum divisor cordial labeling is called a
sum divisor cordial graph. A decomposition of G is a collection   S r H ,H ,.....H 1 2   such
that i H are edge disjoint and every edges in i H belongs to G . If each i H is a sum divisor
cordial graphs, then S  is called a sum divisor cordial decomposition of G . The minimum
cardinality of a sum divisor cordial decomposition of G is called the sum divisor cordial
decomposition number of G and it is denoted by (G). S  In this paper we define sum
divisor cordial decomposition and sum divisor cordial decomposition number (G) S 
of a
graphs. Also investigate some bounds of (G) S 
in product graphs like Cartesian product,
composition etc.

Keywords