On Valuation of Edge Irregularity Strength of Certain Graphical Families

This article comprises of exact valuation of a graph parameter, known as the edge irregularity strength EIS, symbolized as eisG, of various graphical families such as middle graph of path graph, middle graph of cycle graph, snake graph (string 2), paramedian ladder, and complete m-partite graphs. If δ:V⟶1,2,…,p is a function defined on vertices of a graph that helps to determine different weights for every pair of edges, the least value of p is the target. Thus, addition operation for allocated to vertices of an edge, i.e., δvi+δvj, i≠j=1,2,…,n, defines the weight wδvivj of corresponding edge for every vivj∈E. If two different edges ei and ej in graph G carry weights in different manner, i.e., wδei≠wδei for i≠j. Then the edge irregular p-labeling is defined after a vertex p-labeling of G. After establishing various novel results and making some conclusions, an open problem is mentioned in the end.