SOME RESULTS ON GRACEFUL CENTERS OF [P.sub.n] AND RELATED [alpha]-GRACEFUL GRAPHS

In this paper, we have proved that the graph obtained by joining two copies of a bipartite graceful graph by an edge with any two corresponding vertices of both the copies of graphs is [alpha]-graceful. We also proved path step tree and path double step tree are [alpha]-graceful and the graph [P.sub...

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Published inTWMS journal of applied and engineering mathematics Vol. 12; no. 3; p. 908
Main Authors Makadia, H.M, Kaneria, V.J, Andharia, P, Jadeja, D
Format Journal Article
LanguageEnglish
Published Turkic World Mathematical Society 01.07.2022
Subjects
Graph theory
Mathematical research
India
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ISSN2146-1147

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Abstract In this paper, we have proved that the graph obtained by joining two copies of a bipartite graceful graph by an edge with any two corresponding vertices of both the copies of graphs is [alpha]-graceful. We also proved path step tree and path double step tree are [alpha]-graceful and the graph [P.sub.m] * [P.sub.n] * [P.sub.2] is [alpha]-graceful. Graceful center of graceful graph defined. We also found some some graceful centers of path [P.sub.n]. Acharya and Gill [1] proved [P.sub.n] * [P.sub.m] is [alpha]-graceful. In this paper we proved its generalized result. Keywords: Graceful center of a graceful graph, universal graceful graph, [alpha]-graceful graph, Path step tree, Path double step tree. AMS Subject Classification: 05C78.
AbstractList In this paper, we have proved that the graph obtained by joining two copies of a bipartite graceful graph by an edge with any two corresponding vertices of both the copies of graphs is [alpha]-graceful. We also proved path step tree and path double step tree are [alpha]-graceful and the graph [P.sub.m] * [P.sub.n] * [P.sub.2] is [alpha]-graceful. Graceful center of graceful graph defined. We also found some some graceful centers of path [P.sub.n]. Acharya and Gill [1] proved [P.sub.n] * [P.sub.m] is [alpha]-graceful. In this paper we proved its generalized result. Keywords: Graceful center of a graceful graph, universal graceful graph, [alpha]-graceful graph, Path step tree, Path double step tree. AMS Subject Classification: 05C78.
In this paper, we have proved that the graph obtained by joining two copies of a bipartite graceful graph by an edge with any two corresponding vertices of both the copies of graphs is [alpha]-graceful. We also proved path step tree and path double step tree are [alpha]-graceful and the graph [P.sub.m] * [P.sub.n] * [P.sub.2] is [alpha]-graceful. Graceful center of graceful graph defined. We also found some some graceful centers of path [P.sub.n]. Acharya and Gill [1] proved [P.sub.n] * [P.sub.m] is [alpha]-graceful. In this paper we proved its generalized result.
Audience Academic
Author Jadeja, D
Andharia, P
Makadia, H.M
Kaneria, V.J
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Mathematical research
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