In this paper, we introduce a new labeling namely ‘edge k-product cordial labeling’ as
follows: For a graph G = (V (G), E(G)) having no isolated vertex, an edge labeling f : E(G) →
{0, 1, ..., k − 1}, where k > 1 is an integer, is said to be an edge k-product cordial labeling if it
induces a vertex labeling f
⋆
: V (G) → {0, 1, ..., k − 1} defined by f
⋆
(v) =
Q
f(uv)(mod k)
satisfies |e
f
(i) − e
f
(j)| ≤ 1 and |v
f
⋆
(i) − v
f
uv∈E(G)
⋆
(j)| ≤ 1 for i, j ∈ {0, 1, ..., k − 1}, where e
(i) and
v
⋆
(i) denote the number of edges and vertices respectively having a label i (i = 0, 1, ..., k − 1).
Further, we study the edge k-product cordial behavior of star, bistar, shadow and splitting graph
of star, path union of star, bistar and cycle graphs. |
