Abstract:
A set D of vertices in a graph G = (V, E) is a dominating set of (j if every vertex in
V-D is adjacent to some vertex in D. The domination number of G i, the minimum
cardinality taken over all minimal dominating sets in G and is denoted by y(G). The
nonbondage number of a graph G is the maximum cardinality among all sets of
edges X <;; E(G) such iliat y(G~X)=y(G) and it is denoted by bll(G).IIIth~ same way,
we call define total dominalJon number, eonnect~d domination number, global
domination number and total global domination number of graphs. DilTerent types of
methods arc available depending on types of the problems. Some exact values for the
nonhondage number of graphs arc found. Upper bounds are ohtained for nonbondage
number of a graph and the exact values ure determined for s~v~ral c1asse<;of graphs.
\Ve have illustrated with examples some various results for the connected
domillation number of graphs of standard graphs with better explanation.The exact
values of connected domination nnmber and global domination number for somc
standard graphs are calculated with the help of methods used by Kulli,
Shampathkumar, Janakiram etc, We hav~ abo establi,hed some theorems relaled
with the total global domination number of graph"
In order to minimize the direct communication links among the transmitting stations
under communication networks where maximum number of links that should be
dropped to aeeompli,h this task is the nonboodage of a graph.
In th~ similar way we can also apply eonnect~d domination number and total global
domination number in various 'ways.
