GRACEFUL COLORING OF LADDER GRAPHS

A graceful k-coloring of a non-empty graph G = (V, E) is a proper vertex coloring f : V(G) [right arrow] {1,2,...,k}, k [greater than or equal to] 2, which induces a proper edge coloring f*: E(G) [right arrow] {1,2,...,k-1} defined by f*(uv) = |f(u)-f(v)|, where u,v [member of] V(G). The minimum k f...

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Bibliographic Details
Published in:TWMS journal of applied and engineering mathematics 2024-07, Vol.14 (3), p.991
Main Authors: Laavanya, D, Yamini, S. Devi
Format: Article
Language:English
Subjects:
Analysis
Functional analysis
Graph coloring
Graph theory
Graphs
Labeling
Mathematics
Methods
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Summary:A graceful k-coloring of a non-empty graph G = (V, E) is a proper vertex coloring f : V(G) [right arrow] {1,2,...,k}, k [greater than or equal to] 2, which induces a proper edge coloring f*: E(G) [right arrow] {1,2,...,k-1} defined by f*(uv) = |f(u)-f(v)|, where u,v [member of] V(G). The minimum k for which G has a graceful k-coloring is called graceful chromatic number, [x.sub.g](G). The graceful chromatic number for a few variants of ladder graphs are investigated in this article. KEYWORDS: Graceful chromatic number, ladder graphs.
ISSN:2146-1147
2146-1147