2025/09/13 by Jason D. Andoyo, Andoyo, Jason
Computer Science · #05C78 #11A07 #11A15 #Blockchain Technology in Education and Learning #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems
paper · pdf · doi:10.48550/arxiv.2509.11012
openalex publication_date 2025/09/13 · openalex created_date 2025/10/12 · openalex updated_date 2026/07/28
For a simple connected graph G of order n, a bijective function f:V(G)→\1,2,⋯,n\ is said to be a Legendre cordial labeling modulo p, where p is an odd prime, if the induced function fp^*:E(G)→ \0,1\, defined by fp^*(uv)=0 whenever ([f(u)+f(v)]/p)=-1 or f(u)+f(v)≡ 0(mod p), and fp^*(uv)=1 whenever ([f(u)+f(v)]/p)=1, satisfies the condition |efp^*(0)-efp^*(1)|≤ 1 where efp^*(i) is the number of edges with label i (i=0,1). This paper investigates the Legendre cordial labeling of graphs obtained through various operations: join, corona, lexicographic product, cartesian product, tensor product, and strong product.