Matching in Semigraph

In this paper, the well known concept of matching of graph theory has been discussed in the setting of semigraphs resulting in few new concepts like maximal vertex-saturated matching, minimal edge-saturated matching and optimum matching which have no parallels in graphs. In this connection, we record a number of characterizations of maximum matching and other related terms of semigraphs developed here and also establish parallels of theorems due to Berge and König for graphs. A new concept on total adjacent domination in connection with adjacent domination in semigraph as studied by Kamath and Bhat [7] is introduced here and few results are developed that establish links between adjacent domination number and total adjacent domination number as well as between total adjacent domination number and minimal edge-saturated matching. The matching is one of the most interesting and well-studied concept in Graph Theory and it has vast applications in real world situations. One of the most significant results about this concept is due to C. Berge [4], which gives the characterization of a maximum