Graceful Coloring of Ladder Graphs

2022/11/29 by Laavanya, D, Yamini, S Devi
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2211.15904

Abstract

A graceful k-coloring of a non-empty graph G=(V,E) is a proper vertex coloring f:V(G)→\lbrace 1,2,...,k \rbrace, k≥ 2, which induces a proper edge coloring f^*:E(G)→\lbrace 1, 2, . . . , k-1 \rbrace defined by f^*(uv) = |f(u)-f(v)|, where u,v∈ V(G). The minimum k for which G has a graceful k-coloring is called graceful chromatic number, χ_g(G). The graceful chromatic number for a few variants of ladder graphs are investigated in this article.

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