منابع مشابه
Genus Distributions for Iterated Claws
We derive a recursion for the genus distributions of the graphs obtained by iteratively attaching a claw to the dipole D3. The minimum genus of the graphs in this sequence grows arbitrarily large. The families of graphs whose genus distributions have been calculated previously are either planar or almost planar, or they can be obtained by iterative single-vertex or single-edge amalgamation of s...
متن کاملIterated Claws Have Real-rooted Genus Polynomials
We prove that the genus polynomials of the graphs called iterated claws are real-rooted. This continues our work directed toward the 25-year-old conjecture that the genus distribution of every graph is log-concave. We have previously established log-concavity for sequences of graphs constructed by iterative vertexamalgamation or iterative edge-amalgamation of graphs that satisfy a commonly obse...
متن کاملGenus Distributions of Iterated 3-Wheels and 3-Prisms
The iterated 3-prism Pr 3 is the cartesian product C32Pn of a 3-cycle and an n-vertex path. At each end of the iterated 3-prism, there is a 3-cycle whose vertices are 3-valent in C32Pn. The iterated 3-wheel W 3 is obtained by contracting one of these 3-cycles in C32Pn+1 to a single vertex. Using rooted-graphs, we derive simultaneous recursions for the partitioned genus distributions of W 3 and ...
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What are the early signs of use? There are no early signs. There are only obvious signs common to all long-term users. What can be spotted is the transition from non-user to addict (one episode is sufficient for diagnosis). For example, an early draft of a manuscript may read “We replicated and extended a classic finding within an established theoretical framework...”; a later SciagraTM-influen...
متن کاملGenus distributions of star-ladders
Star-ladder graphs were introduced by Gross in his development of a quadratic-time algorithm for the genus distribution of a cubic outerplanar graph. This paper derives a formula for the genus distribution of star-ladder graphs, using Mohar’s overlap matrix and Chebyshev polynomials. Newly developed methods have led to a number of recent papers that derive genus distributions and total embeddin...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2014
ISSN: 1077-8926
DOI: 10.37236/2278