Abstract
Let G be a (p, q)-graph. Let f be an injective mapping from V(G) to {1, 2, …, p}. For each edge xy, assign the label left(genfrac{}{}{0pt}{}{x}{y}right) or left(genfrac{}{}{0pt}{}{y}{x}right) according as x > y or y > x. Call f a parity combination cordial labeling if |ef(0) − ef(1)| ≤ 1, where ef(0) and ef(1) denote the number of edges labeled with an even number and an odd number, respectively. In this paper we make a survey on all graphs of order at most six and find out whether they satisfy a parity combination cordial labeling or not and get an upper bound for the number of edges q of any graph to satisfy this condition and describe the parity combination cordial labeling for two families of graphs.
Highlights
In this paper we will deal with finite simple undirected graphs
By G(V, E) we mean a graph with p vertices and q edges, where p = |V| and q = |E|
Call f a parity combination cordial labeling if |ef(0) − ef(1)| ≤ 1, where ef(0) and ef(1) denote the number of edges labeled with an even number and an odd number, respectively
Summary
In this paper we will deal with finite simple undirected graphs. By G(V, E) we mean a graph with p vertices and q edges, where p = |V| and q = |E|. They proved that Wn admits a parity combination cordial labeling if and only if n ≥ 4, and conjectured that for n ≥ 4, Kn is not a parity combination cordial graph.
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