Study of Mean Labelings on Product Graphs
Current Topics on Mathematics and Computer Science Vol. 7,
5 August 2021
,
Page 8-16
https://doi.org/10.9734/bpi/ctmcs/v7/3317F
Abstract
Let G be a(p,q) graph and let: \(V(G) \rightarrow\) {O,1,…,q} be an injection. Then G is said to have a mean labeling if for each edge uv, there exists an induced injective map \(f^*:E(G) \rightarrow\) {1,2,…,q} defined by
\(f^* (uv)= {f(u) + f(v) \over 2}\) if \(f(u)+f(v)\) is even
\(= {f(u) + f(v) + 1 \over 2}\) if \(f(u)+f(v)\) is odd
The graph G is said to be a near mean graph if the injective map f : V(G)\(\rightarrow\){1,2,…,q-1,q+1} induces \(f^*:E(G)\rightarrow\){1,2,…,q} which is also injective, defined as above. In this paper , We looked at the direct product of paths and augmented star graphs for their mean labelings and the Cartesian product of Pn and K4 for its near- meanness in labelings.
- Mean graph
- near-mean graph
- direct product
- Cartesian product