Edge Sum Divisor Cordial Labeling of Some Graphs with Python Implementation

Abstract

Let Ω = (W(Ω), F(Ω)) be a graph that has neither loop nor multiple edges, where W(Ω) represents the node set and F(Ω) represents the line set and let h: F(Ω) → {1, 2, . . . |F(Ω)|} be a bijection. For each node u, give it a label of 1 if 2 | h(b₁) + h(b₂) +...+ h(b_s) and 0 if it doesn't where b₁, b₂, . . . b_s are lines that are incident with the node u. If the difference between nodes categorized 0 and 1 is less than or equal to 1, the function h is called ESDC labelling. An ESDC graph is one that has the ESDC labeling. In this paper, we prove the circular ladder graph CLs when s is even, the subdivision of the star S(K_1,s), the bistar graph B_s.s when s is odd and the star graph K_1,s when s is even are ESDC graphs. Also in this paper, we investigate an edge sum divisor cordial labeling of the above graphs using python language.