The Edge Odd Graceful Labeling of Water Wheel Graphs - Mohammed Aljohani; Salama Nagy Daoud (Axioms)
A graph, <semantics>G=(V,E)</semantics>, is edge odd graceful if it possesses edge odd graceful labeling. This labeling is defined as a bijection <semantics>g:E(G)→{1,3,…,2m−1}</semantics>, from which an injective transformation is derived, <semantics>g*:V(G)→{1,2,3,…,2m−1}</semantics>, from the rule that the image of <semantics>u∈V(G)</semantics> under <semantics>g*</semantics> is <semantics>∑uv∈E(G)g(uv)<mspace width="0.277778em"></mspace>mod<mspace width="0.277778em"></mspace>(2m)</semantics>. The main objective of this manuscript is to introduce new classes of planar graphs, namely water wheel graphs, <semantics>WWn</semantics>; triangulated water wheel graphs, <semantics>TWn</semantics>; closed water wheel graphs, <semantics>CWn</semantics>; and closed triangulated water wheel graphs, <semantics>CTn</semantics>. Furthermore, we specify conditions for these graphs to allow for edge odd graceful labelings.