HARMONIC MEAN LABELING OF H-SUPER SUBDIVISION OF PATH GRAPHS

S. Meena and M. Sivasakthi

  DOI:
  https://doi.org/10.37418/amsj.9.4.73

Full Text

A graph $G$ with $p$ vertices and $q$ edges is called a harmonic mean graph if it is possible to label the vertices $x\in V$ with distinct labels $f(x)$ from $\{1,2,…q+1\}$ in such a way that each edge $e = uv$ is labeled with $$f(uv)=\left\lceil \frac{2f(u)f(v)}{f(u)+f(v)}\right\rceil \quad \text{(or)} \quad \left\lfloor \frac{2f(u)f(v)}{f(u)+f(v)}\right\rfloor$$ then the edge labels are distinct. In this case $f$ is called Harmonic mean labeling of $G$. In this paper we prove that some families of graphs such as H- super subdivision of path $HSS(P_n)$, $HSS(P_n)\odot K_1,$ $HSS(P_n)\odot \overline{K_2}$, $HSS(P_n)\odot K_2$ are harmonic mean graphs.


Keywords:
Harmonic mean graph, H-super subdivision of path $HSS(P_n)$, $HSS(P_n)\odot K_1,$ $HSS(P_n)\odot \overline{K_2}$, $HSS(P_n)\odot K_2$.