The Edge Odd Graceful Labeling of Water Wheel Graphs

被引：0

作者：

Aljohani, Mohammed ^{[1
]}

Daoud, Salama Nagy ^{[1
,2
]}

机构：

[1] Taibah Univ, Fac Sci, Dept Math, Al Madinah 41411, Saudi Arabia

[2] Menoufia Univ, Fac Sci, Dept Math & Comp Sci, Shibin Al Kawm 32511, Egypt

来源：

AXIOMS | 2025年 / 14卷 / 01期

关键词：

graceful labeling; edge graceful labeling; edge odd graceful labeling; water wheel graph;

D O I：

10.3390/axioms14010005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A graph, G=(V,E), is edge odd graceful if it possesses edge odd graceful labeling. This labeling is defined as a bijection g:E(G)->{1,3,& mldr;,2m-1}, from which an injective transformation is derived, g*:V(G)->{1,2,3,& mldr;,2m-1}, from the rule that the image of u is an element of V(G) under g* is & sum;uv is an element of E(G)g(uv)mod(2m). The main objective of this manuscript is to introduce new classes of planar graphs, namely water wheel graphs, WWn; triangulated water wheel graphs, TWn; closed water wheel graphs, CWn; and closed triangulated water wheel graphs, CTn. Furthermore, we specify conditions for these graphs to allow for edge odd graceful labelings.

引用

页数：17

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