Circular wirelength of Generalized Petersen Graphs
نویسندگان
چکیده
In this paper we formulate the Vertex Congestion Lemma leading to a new technique in computing the exact wirelength of an embedding. We compute the circular wirelength of generalized Petersen graphs by partitioning the vertices as well as the edges of cycles. Further we obtain the linear wirelength of circular ladders. Our algorithms produce optimal values in linear time.
منابع مشابه
Wirelength of 1-fault hamiltonian graphs into wheels and fans
In this paper we obtain a fundamental result to find the exact wirelength of 1-fault hamiltonian graphs into wheels and fans. Using this result we compute the exact wirelength of circulant graphs, generalized petersen graphs, augmented cubes, crossed cubes, mőbius cubes, locally twisted cubes, twisted cubes, twisted n-cubes, generalized twisted cubes, hierarchical cubic networks, alternating gr...
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 کاملThe lower bound for the number of 1-factors in generalized Petersen graphs
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 کاملAn Edge-Isoperimetric Problem for Powers of the Petersen Graph
In this paper we introduce a new order on the set of n-dimensional tuples and prove that this order preserves nestedness in the edge isoperimetric problem for the graph Pn, defined as the nth cartesian power of the well-known Petersen graph. The cutwidth and wirelength of Pn are also derived. These results are then generalized for the cartesian product of Pn and the m-dimensional binary hypercube.
متن کاملA Dynamic View of Circular Colorings
The main contributions of this paper are three-fold. First, we use a dynamic approach based on Reiter’s pioneering work on Karp-Miller computation graphs [19] to give a new and short proof of Mohar’s Minty-type Theorem [15]. Second, we bridge circular colorings and discrete event dynamic systems to show that the Barbosa and Gafni’s results on circular chromatic number [5, 21] can be generalized...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Journal of Interconnection Networks
دوره 12 شماره
صفحات -
تاریخ انتشار 2011