Enumeration of Hamiltonian cycles in certain generalized Petersen graphs
نویسندگان
چکیده
منابع مشابه
Hyper-Hamiltonian generalized Petersen graphs
Assume that n and k are positive integers with n ≥ 2k + 1. A non-hamiltonian graph G is hypo hamiltonian if G − v is hamiltonian for any v ∈ V (G). It is proved that the generalized Petersen graph P (n, k) is hypo hamiltonian if and only if k = 2 and n ≡ 5 (mod 6). Similarly, a hamiltonian graph G is hyper hamiltonian if G−v is hamiltonian for any v ∈ V (G). In this paper, we will give some nec...
متن کاملThe classification of hamiltonian generalized Petersen graphs
The generalized Petersen graph GP(n, k), n > 2 and 1 < k & n 1, has vertex-set (uO,ul ,..., u *-,, vO,u ,,..., v,_,) and edge-set (u,ui+,,uioi,vivi+,:O 8.
متن کاملOn certain Hamiltonian cycles in planar graphs
The problem is considered under which conditions a 4-connected planar or projective planar graph has a Hamiltonian cycle containing certain prescribed edges and missing certain forbidden edges. The results are applied to obtain novel lower bounds on the number of distinct Hamiltonian cycles that must be present in a 5-connected graph that is embedded into the plane or into the projective plane ...
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...
متن کاملOn the crossing numbers of certain generalized Petersen graphs
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1989
ISSN: 0095-8956
DOI: 10.1016/0095-8956(89)90064-6