DISCOVERY OF DIFFERENT GRAPHS INTO PRIME GRAPHS

Abstract

A collection that is edge disjoint and all of its edges belong to is referred to as a decomposition of. It is referred to as a prime
decomposition of if every graph is a prime graph. . The minimum cardinality among the minimal ID set is called an ID number of
G(V,E)
and it is denoted by
? ?(G).
Further study the inverse domination number
? ?(G).
of complete and complete bipartite IFG
some results and also identify some bounds of the ID-number are investigated. The ID-number of some standard operations join of two IFGs
and Cartesian product of two IFG are investigated. Some results like
G(V,E)
is an IFG without isolated vertices, then
? (G) ?? ?(G)
.
The IFG
G(V,E)
be a complete IFG, then
G u if ?
?
? ( )
, here u is the vertex having the second minimum cardinality in
G(V,E)
.AnIFG
G(A,B)
be a complete bipartite IFG, then
G u v if ? ?
?
? ( )
, here u and v are the vertex having the second minimum
cardinality in vertices set 1 2 V and V
in
G(V,E)
.