DOI: https://doi.org/10.14710/jfma.v4i2.11607

SOME CARTESIAN PRODUCTS OF A PATH AND PRISM RELATED GRAPHS THAT ARE EDGE ODD GRACEFUL

*Yeni Susanti  -  Dept. of Mathematics, Gadjah Mada University, Indonesia
Iwan Ernanto  -  Dept. of Mathematics, Gadjah Mada University, Indonesia
Aluysius Sutjijana  -  Dept. of Mathematics, Gadjah Mada University, Indonesia
Sufyan Sidiq  -  Dept. of Mathematics, Gadjah Mada University, Indonesia

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Abstract

Let $G$ be a connected undirected simple graph of size $q$ and let $k$ be the maximum number of its order and its size. Let $f$ be a bijective edge labeling which codomain is the set of odd integers from 1 up to $2q-1$. Then $f$ is called an edge odd graceful on $G$ if the weights of all vertices are distinct, where the weight of a vertex $v$ is defined as the sum $mod(2k)$ of all labels of edges incident to $v$. Any graph that admits an edge odd graceful labeling is called an edge odd graceful graph. In this paper, some new graph classes that are edge odd graceful are presented, namely some cartesian products of path of length two and some circular related graphs.

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Keywords: edge odd graceful graphs; edge odd graceful labeling; cycle; prism graphs; antiprism graphs; path; cartesian product

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Section: FUNDAMENTAL MATHEMATICS AND APPLICATIONS
Language : EN
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