In this paper we unify several existing regularity conditions for graphs, including strong regularity, k-isoregularity, and the t-vertex condition. We develop an algebraic composition/decomposition theory of conditions. Using our theoretical results show that a family non rank 3 graphs known to satisfy 7-vertex condition fulfills even stronger condition, (3,7)-regularity (the notion is defined ...

In this research paper, we present a novel frame work for handling $m$-polar information by combining the theory of $m-$polar fuzzy  sets with graphs. We introduce certain types of edge regular $m-$polar fuzzy graphs and edge irregular $m-$polar fuzzy graphs. We describe some useful properties of edge regular, strongly edge irregular and strongly edge totally irregular $m-$polar fuzzy graphs. W...