SIGNED SUM CORDIAL LABELING OF GRAPHS

SIGNED SUM CORDIAL LABELING OF GRAPHS

K. Jeya Daisy, P. Princy Paulson, P. Jeyanthi

[PDF]

Abstract

The notion of signed product cordial labeling was introduced in 2011 and further studied by several researchers. Inspired by this notion, we define a new concept namely signed sum cordial labeling as follows: A vertex labeling of a graph G, f : V (G) → {−1, +1} with induced edge labeling f∗ : E(G) → {−2, 0, +2} defined by f∗(uv) = f(u) + f(v) is signed sum cordial labeling if |vf (−1) − vf(+1)| ≤ 1 and |ef∗ (i) − ef∗ (j)| ≤ 1 for i, j ∈ {−2, 0, +2}, where vf (−1) is the number of vertices labeled with -1, vf(+1) is the number of vertices labeled with +1, ef∗ (−2) is the number of edges labeled with -2, ef∗ (0) is the number of edges labeled with 0 and ef∗(+2) is the number of edges labeled with +2. A graph G is signed sum cordial if it admits signed sum cordial labeling. In this paper, we investigate the signed sum cordial behaviour of some standard graphs.

Keywords

cordial labeling, signed cordial labeling, signed product cordial labeling, signed sum cordial labeling.