Graceful Coloring of Ladder Graphs
A graceful k-coloring of a non-empty graph $G=(V,E)$ is a proper vertex coloring $f:V(G)\rightarrow\lbrace 1,2,...,k \rbrace$, $k\geq 2$, which induces a proper edge coloring $f^{*}:E(G)\rightarrow\lbrace 1, 2, . . . , k-1 \rbrace $ defined by $f^{*}(uv) = |f(u)-f(v)|$, where $u,v\in V(G)$. The mini...
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| creator | Laavanya, D Yamini, S Devi |
| description | A graceful k-coloring of a non-empty graph $G=(V,E)$ is a proper vertex
coloring $f:V(G)\rightarrow\lbrace 1,2,...,k \rbrace$, $k\geq 2$, which induces
a proper edge coloring $f^{*}:E(G)\rightarrow\lbrace 1, 2, . . . , k-1 \rbrace
$ defined by $f^{*}(uv) = |f(u)-f(v)|$, where $u,v\in V(G)$. The minimum $k$
for which $G$ has a graceful $k$-coloring is called graceful chromatic number,
$\chi_{g}(G)$. The graceful chromatic number for a few variants of ladder
graphs are investigated in this article. |
| doi_str_mv | 10.48550/arxiv.2211.15904 |
| format | Article |
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coloring $f:V(G)\rightarrow\lbrace 1,2,...,k \rbrace$, $k\geq 2$, which induces
a proper edge coloring $f^{*}:E(G)\rightarrow\lbrace 1, 2, . . . , k-1 \rbrace
$ defined by $f^{*}(uv) = |f(u)-f(v)|$, where $u,v\in V(G)$. The minimum $k$
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coloring $f:V(G)\rightarrow\lbrace 1,2,...,k \rbrace$, $k\geq 2$, which induces
a proper edge coloring $f^{*}:E(G)\rightarrow\lbrace 1, 2, . . . , k-1 \rbrace
$ defined by $f^{*}(uv) = |f(u)-f(v)|$, where $u,v\in V(G)$. The minimum $k$
for which $G$ has a graceful $k$-coloring is called graceful chromatic number,
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coloring $f:V(G)\rightarrow\lbrace 1,2,...,k \rbrace$, $k\geq 2$, which induces
a proper edge coloring $f^{*}:E(G)\rightarrow\lbrace 1, 2, . . . , k-1 \rbrace
$ defined by $f^{*}(uv) = |f(u)-f(v)|$, where $u,v\in V(G)$. The minimum $k$
for which $G$ has a graceful $k$-coloring is called graceful chromatic number,
$\chi_{g}(G)$. The graceful chromatic number for a few variants of ladder
graphs are investigated in this article.</abstract><doi>10.48550/arxiv.2211.15904</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Combinatorics |
| title | Graceful Coloring of Ladder Graphs |
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