Annals of Communications in Mathematics

ABSTRACT.An injective function \( f : V(G) \to \{T_0, T_1, T_2, \ldots, T_n\} \), where \( n = |V(G)| - 1 \), is said to be a Tribonacci cordial labeling if the induced function \( f^{*} : E(G) \to \{0,1\} \) defined by \( f^{*}(uv) = (f(u) + f(v)) \pmod 2 \) satisfies the condition \( |e_f(0) - e_f(1)| \le 1 \), where \( e_f(0) \) is the number of edges with label \( 0 \) and \( e_f(1) \) is the number of edges with label \( 1 \). A graph that admits such labeling is called a Tribonacci cordial graph. In this paper, we determine the Tribonacci cordial labeling of Triangular Snake Graph \( TS_n \), Double Triangular Snake Graph \( DT(S_n) \), Quadrilateral Snake Graph \( QS_n \), Double Quadrilateral Snake Graph \( D(QS_n) \), and Cycle Quadrilateral Snake Graph \( C(QS_n) \).

Abstract: Let \( G \) be a graph. An Edouard Product Cordial Labeling (EPCL) of a graph \( G \) with \( |V(G)| = n \) is an injective function \( f : V(G) \rightarrow \{E_0, E_1, E_2, \ldots, E_{n-1}\} \) where \( E_i \) is the \( i \)th Edouard number \( (i = 0,1,2,3,\ldots,n) \) that induces a function \( f^* \) defined by\(f^*(uv) = (f(u)f(v)) \; (\text{mod } 2)\) for all edge \( e = uv \) such that \( |e_f^*(0) - e_f^*(1)| \leq 1 \) where \( e_f^*(0) \) is the number of vertices labeled with 0 and \( e_f^*(1) \) is the number of vertices labeled with 1. The graph that satisfies the condition of an edouard product cordial labeling is called an edouard product cordial graph (EPCG).

Abstract:An injective function \( f : V(G) \rightarrow \{L_1, L_2, \ldots, L_n\} \), where \( L_i \) is the \( i \)th Lucas number, is called a Lucas product cordial labeling if the induced function satisfies \( |e_f^*(0) - e_f^*(1)| \leq 1 \). A graph which admits Lucas product cordial labeling is called Lucas product cordial graph. In this paper, we determined the Lucas Product Cordial Labeling of Quadrilateral Snake Graph Qn, Cycle Quadrilateral Snake Graph CQn, and Alternate Triangular Snake Graph A(Tn).