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Communication in Combinatorics and Optimization، جلد ۱۰، شماره ۴، صفحات ۹۳۳-۹۴۸
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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 |
The crossing numbers of join products of $K_4cup K_1$ with cycles |
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| چکیده انگلیسی مقاله |
The crossing number $mathrm{cr}(G)$ of a graph $G$ is the minimum number of edge crossings over all drawings of $G$ in the plane. In the paper, we extend known results concerning crossing numbers of join products of two small graphs with cycles. The crossing number of the join product $G^ast + C_n$ for the disconnected graph $G^ast$ consisting of the complete graph $K_{4}$ and one isolated vertex is given, where $C_n$ is the cycle on $n$ vertices. The proof of the main result is done with the help of lemma whose proof is based on a special redrawing technique. Up to now, the crossing numbers of $G + C_n$ were done only for a few disconnected graphs $G$. Finally, by adding new edge to the graph $G^ast$, we are able to obtain the crossing number of $G_1+C_n$ for one other graph $G_1$ of order five. |
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| کلیدواژه‌های انگلیسی مقاله |
graph,crossing number,join product,separating cycle,cycle |
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| نویسندگان مقاله |
Michal Staš |
Department of Mathematics and Theoretical Informatics,
Faculty of Electrical Engineering and Informatics,
Technical University, 042 00 Košice, Slovak Republic
Maria Timková |
Department of Mathematics and Theoretical Informatics,
Faculty of Electrical Engineering and Informatics,
Technical University, 042 00 Košice, Slovak Republic
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| نشانی اینترنتی |
https://comb-opt.azaruniv.ac.ir/article_14732_3ee57576d44ffa0d3a4f74d7b688f3fe.pdf |
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| زبان مقاله منتشر شده |
en |
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