The crossing number of the generalized Petersen graph $P[3k,k]$
نویسندگان
چکیده
منابع مشابه
The crossing number of the generalized Petersen graph P(10, 3) is six
The crossing number of a graph is the least number of crossings of edges among all drawings of the graph in the plane. In this article, we prove that the crossing number of the generalized Petersen graph P (10, 3) is equal to 6.
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In this paper, we investigate the number of 1-factors of a generalized Petersen graph $P(N,k)$ and get a lower bound for the number of 1-factors of $P(N,k)$ as $k$ is odd, which shows that the number of 1-factors of $P(N,k)$ is exponential in this case and confirms a conjecture due to Lovász and Plummer (Ann. New York Acad. Sci. 576(2006), no. 1, 389-398).
متن کاملGraceful labelings of the generalized Petersen graphs
A graceful labeling of a graph $G=(V,E)$ with $m$ edges is aninjection $f: V(G) rightarrow {0,1,ldots,m}$ such that the resulting edge labelsobtained by $|f(u)-f(v)|$ on every edge $uv$ are pairwise distinct. For natural numbers $n$ and $k$, where $n > 2k$, a generalized Petersengraph $P(n, k)$ is the graph whose vertex set is ${u_1, u_2, cdots, u_n} cup {v_1, v_2, cdots, v_n}$ and its edge set...
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McQuillan, D. and R.B. Richter, On the crossing numbers of certain generalized Petersen graphs, Discrete Mathematics 104 (1992) 311-320. In his paper on the crossing numbers of generalized Petersen graphs, Fiorini proves that P(8, 3) has crossing number 4 and claims at the end that P(10, 3) also has crossing number 4. In this article, we give a short proof of the first claim and show that the s...
متن کاملOn the Independence Number of the Generalized Petersen Graph P(n,k)∗
Let G = (V (G),E(G)) be a simple finite undirected graph. A set S ⊆ V (G) is an independent set if no two vertices of S are adjacent. The independence number α(G) is the maximum cardinality of an independent set in G. In this paper, we investigate the independence number of generalized Petersen graph, and give the exact values of P(n,k) for k = 1,2,3,5.
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ژورنال
عنوان ژورنال: Mathematica Bohemica
سال: 2003
ISSN: 0862-7959,2464-7136
DOI: 10.21136/mb.2003.134001