To Find the Comparison of Non-Split Domination Number, The Average Distance and The Diameter of Circular-Arc Graphs

Abstract

A connected dominating set is used as a backbone for communications and vertices that are not in this set communicate by passing
message through neighbors that are in the set. Among the various applications of the theory of domination and the distance, the most often
discussed is a communication network. This network consists of communication links all distance between affixed set of sites. Circular-arc
graphs are rich in combinatorial structures and have found applications in several disciplines such as Biology, Ecology, Psychology, Traffic
control, Genetics, Computer sciences and particularly useful in cyclic scheduling and computer storage allocation problems etc. Suppose
communication network does not work due to link failure. Then the problem is what is the fewest number of communication links such that at
least one additional transmitter would be required in order that communication with all sites as possible. This leads to the introducing of the
concept of the non-split domination number, average distance and diameter. In this paper we present the comparison of non-split domination
number, the average distance and the diameter of circular-arc graphs.