On (α, β)-Total Edge Irregularity Strength of Some Graphs

Abstract

Let , and  having cardinality  and  respectively, symbolize the vertex set, and edge set of a simple graph  together with a total – labeling  where . Let . If an invertible function exists, say  specified by  for every edge  with , then is termed as total edge irregular labeling. Also, the value  is said to be the edge weight of .  The least  for which  admits  – edge irregular  is indicated by , known as Total Edge irregularity Strength of the graph The precise value of for standard graph families and Mycielskian path graphs is explored in this work. In addition, an open problem of  and are solved partially.