In graph theory, a connected component of an undirected graph is a sub graph in which any two vertices are connected to each other by paths. For a graph G, if the sub graph of G itself is a connected component then the graph is called connected, else the graph G is called disconnected and each connected component sub graph is called it’s components. Circular-arc graphs have variety of applications involving traffic light sequencing, genetics etc. A dominating set D of graph G = (V,E) is a non-split dominating set if the induced sub graph < V-D > is connected. The non-split domination number ns(G) of G is the minimum cardinality of a non-split dominating set .In this paper constructed an algorithm for finding a non-split dominating set of an Circular-Arc graph. Also its relationships with other parameters is investigated.
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