E-Cordial Labeling of Some Families of Graphs

An E-cordial labeling σ: E →{0,1} induces σ∗: V →{0,1} on graph G=(V,E), where (σ(v)=(∑_(u∈V)▒〖σ(uv)〗) mod 2 is taken over all edges uv∈E, and the labelling satisfies the conditions |vσ (0)-vσ (1)|≤1, |eσ (0)-eσ (1)|≤1. Where vσ (k) represent the count of vertices within the graph G  that bear the label k based on the labeling function  σ (here k can be either 0 or 1). Similarly, eσ∗ (k) denotes the quantity of edges in the graph G that link vertices labeled with the value k according to the labeling function σ∗ (here k can be 0 or 1). A graph along with E-cordial labeling is called an E-cordial graph. We prove that the graphs such as Herschel graph H, Durer graph, Frucht graph, Tietze graph, hypohamiltonian graph, truncated tetrahedron graph, cubic graph with 12 vertices, Wagner graph, Moser spindle graph, Goldner-Harary graph and diamond graph are E-cordial graphs.