Exploring Stolarsky-3 Mean Cordial Labeling Properties in Graph Classes with a Python Module
A. Sasikala · Communications on Applied Nonlinear Analysis · 2025
A graph G= (V,E), where V is the set of vertices and E is the set of edges, with p vertices and q edges. A graph G is referred to as a Stolarsky-3 Mean cordial graph if we can assign distinct labels to each vertex x ∈ V from the set {0,1,2}, denoted by f(x), and distinct labels to each edge e = uv ∈ E based on the values assigned to the endpoints u and v. The label for the edge e = uv is calculated using one of the following Stolarsky-3 Mean cordial formula: The function f is referred to as a Stolarsky-3 mean cordial labeling if the conditions |vf (i) - vf (j)| 1 and |ef (i) - ef (j)| 1. Hold for i, j ɛ{0,1,2 } , where vf(x) and ef(x) represent the number of vertices and edges respectively, labeled with x ( x= 0,1,2 ). A graph that admits such a labeling is called a mean cordial graph. Such that the edge labels are derived from the flooring function of the Stolarsky-3 mean of the labels of the two end vertices of each edge. In this paper, we have created python module to analysis the Stolarsky-3 mean cordial labeling properties of various graph classes, including Path (Pn), Cycle (Cn), Wheel (Wn), Star Graph (K1,n or Sn) & Wheel and Path Graph (WnPm).