Signed sum cordial labeling of graphs

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.