2025/09/11 by Andoyo, J. D. · 1 citation
#05C78 (Primary) #11A07 #11A15 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2509.09528
Let p be an odd prime. 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 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 explores the characterization of the Legendre cordial labeling modulo p of the complete graph Kn using the concept of Legendre graph.