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Communication in Combinatorics and Optimization، جلد ۱۰، شماره ۴، صفحات ۱۰۰۱-۱۰۱۶
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| عنوان فارسی |
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| چکیده فارسی مقاله |
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| کلیدواژه‌های فارسی مقاله |
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| عنوان انگلیسی |
Set colorings of the Cartesian product of some graph families |
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| چکیده انگلیسی مقاله |
Neighbor-distinguishing colorings, which are colorings that induce a proper vertex coloring of a graph, have been the focus of different studies in graph theory. One such coloring is the set coloring. For a nontrivial graph $G$, let $c:V(G)to mathbb{N}$ and define the neighborhood color set $NC(v)$ of each vertex $v$ as the set containing the colors of all neighbors of $v$. The coloring $c$ is called a set coloring if $NC(u)neq NC(v)$ for every pair of adjacent vertices $u$ and $v$ of $G$. The minimum number of colors required in a set coloring is called the set chromatic number of $G$ and is denoted by $chi_s (G)$. In recent years, set colorings have been studied with respect to different graph operations such as join, comb product, middle graph, and total graph. Continuing the theme of these previous works, we aim to investigate set colorings of the Cartesian product of graphs. In this work, we investigate the gap given by $max{ chi_s(G), chi_s(H) } - chi_s(G square H)$ for graphs $G$ and $H$. In relation to this objective, we determine the set chromatic numbers of the Cartesian product of some graph families. |
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| کلیدواژه‌های انگلیسی مقاله |
set coloring,Cartesian product,neighbor-distinguishing coloring |
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| نویسندگان مقاله |
Mark Anthony C. Tolentino |
Department of Mathematics, Ateneo de Manila University, Quezon City, Philippines
Janree Ruark C. Gatpatan |
Department of Mathematics, Ateneo de Manila University, Quezon City, Philippines
Timothy Robin Y. Teng |
Department of Mathematics, Ateneo de Manila University, Quezon City, Philippines
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| نشانی اینترنتی |
https://comb-opt.azaruniv.ac.ir/article_14748_ce982efe80e8c0deed488ac2ebd931d3.pdf |
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| کد مقاله (doi) |
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| زبان مقاله منتشر شده |
en |
| موضوعات مقاله منتشر شده |
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