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On chromatic number and clique number in k-step Hamiltonian graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 4، دوره 9، شماره 1، خرداد 2024، صفحه 37-49 اصل مقاله (416.82 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2022.27970.1407 | ||
| نویسندگان | ||
| Noor A'lawiah Abd Aziz* 1؛ Nader Jafari Rad2؛ Hailiza Kamarulhaili1؛ Roslan Hasni3 | ||
| 1School of Mathematical Sciences , Universiti Sains Malaysia, 11800 Penang, Malaysia | ||
| 2Department of Mathematics, Shahed University, Tehran, Iran | ||
| 3Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, 21030 Kuala Nerus, Terengganu Malaysia | ||
| چکیده | ||
| A graph $G$ of order $n$ is called $k-$step Hamiltonian for $k\geq 1$ if we can label the vertices of $G$ as $v_1,v_2,\ldots,v_n$ such that $d(v_n,v_1)=d(v_i,v_{i+1})=k$ for $i=1,2,\ldots,n-1$. The (vertex) chromatic number of a graph $G$ is the minimum number of colors needed to color the vertices of $G$ so that no pair of adjacent vertices receive the same color. The clique number of $G$ is the maximum cardinality of a set of pairwise adjacent vertices in $G$. In this paper, we study the chromatic number and the clique number in $k-$step Hamiltonian graphs for $k\geq 2$. We present upper bounds for the chromatic number in $k-$step Hamiltonian graphs and give characterizations of graphs achieving the equality of the bounds. We also present an upper bound for the clique number in $k-$step Hamiltonian graphs and characterize graphs achieving equality of the bound. | ||
| کلیدواژه‌ها | ||
| Hamiltonian graph؛ k-step Hamiltonian graph؛ chromatic number؛ clique number | ||
| مراجع | ||
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