Odd Harmonious Labeling of Pn ⊵ C4 and Pn ⊵ D2(C4)

Sabrina Shena Sarasvati (Graph, Combinatorics, and Algebra Research Group, Department of Mathematics, FMIPA, Universitas Jember, Jl. Kalimantan 37 Jember 68121, Indonesia)
Ikhsanul Halikin (Graph, Combinatorics, and Algebra Research Group, Department of Mathematics, FMIPA, Universitas Jember, Jl. Kalimantan 37 Jember 68121, Indonesia)
Kristiana Wijaya (Graph, Combinatorics, and Algebra Research Group, Department of Mathematics, FMIPA, Universitas Jember, Jl. Kalimantan 37 Jember 68121, Indonesia)

Indonesian Journal of Combinatorics
Vol 5, No 2 (2021)

A graph G with q edges is said to be odd harmonious if there exists an injection f:V(G) → ℤ2q so that the induced function f*:E(G)→ {1,3,...,2q-1} defined by f*(uv)=f(u)+f(v) is a bijection.Here we show that graphs constructed by edge comb product of path Pn and cycle on four vertices C4 or shadow of cycle of order four D2(C4) are odd harmonious.