The singularity of m-connected graph

Abstract EN

In this paper we construct a new m-connected graph by the operation joins of two special graphs and the idea of the high-zero sum weighting of vertices is generalized and applied to find the singularity (nullity) of the news mconnected graphs, the new graph constructed by join path with itself and path with cycle of deferent orders, thus some properties are studies of the new m-connected graph and proved that the singularity of a new m-connected graph is the number of non zero distinct independent variables in any of it’s high-zero sum weightings, our goad is to characterizing the singularity of the new m-connected graphs (Pn Pk) , (Pn Ck) and special cases by the new technique of zero sum weighting which studied by cvetkovic and others in [7] and M.Brown in[6].