4 citations · 8 across the 12 of their papers we have counts for
13 papers
On the genera of polyhedral embeddings of cubic graph
Gunnar Brinkmann, Thomas Tucker, Nico Van Cleemput
In this article we present theoretical and computational results on the existence of polyhedral embeddings of graphs. The emphasis is on cubic graphs. We also describe an efficient…
Non-Abelian Simple Groups Act with Almost All Signatures
Mariela Carvacho, Jennifer Paulhus, Tom Tucker +1
The topological data of a group action on a compact Riemann surface is often encoded using a tuple called its signature. There are two easily verifiable arithm…
Distinguishing locally finite trees
Svenja Hüning, Wilfried Imrich, Judith Kloas +2
The distinguishing number of a graph is the smallest number of colors that is needed to color the vertices of such that the only color preserving automorphism is the…
Distinguishing graphs of maximum valence 3
Svenja Hüning, Wilfried Imrich, Judith Kloas +2
The distinguishing number of a graph is the smallest number of colors that is needed to color such that the only color preserving automorphism is the identity. We gi…
Edge-transitive bi-Cayley graphs
Marston Conder, Jin-Xin Zhou, Yan-Quan Feng +1
A graph $\G$ admitting a group of automorphisms acting semi-regularly on the vertices with exactly two orbits is called a {\em bi-Cayley graph\/} over . Such a graph $\G$ is…
The CLLC conjecture holds for cyclic outer permutations
Jonathan L. Gross, Toufik Mansour, Thomas W. Tucker +1
Recently, Gross et al. posed the LLC conjecture for the locally log-concavity of the genus distribution of every graph, and provided an equivalent combinatorial version, the CLLC c…
Root geometry of polynomial sequences II: Type (1,0)
J. L. Gross, T. Mansour, T. W. Tucker +1
We consider the sequence of polynomials defined by the recursion , with initial values and , where $a,b,d,t,…
Root geometry of polynomial sequences I: Type
J. L. Gross, T. Mansour, T. W. Tucker +1
This paper is concerned with the distribution in the complex plane of the roots of a polynomial sequence given by a recursion $W_n(x)=aW_{n-1}(x)+(bx+c)W_{n-2}…
Log-concavity of the genus polynomials of Ringel ladders
J. L. Gross, T. Mansour, T. W. Tucker +1
A Ringel ladder can be formed by a self-bar-amalgamation operation on a symmetric ladder, that is, by joining the root vertices on its end-rungs. The present authors have previousl…
Iterated claws have real-rooted genus polynomials
J. L. Gross, T. Mansour, T. W. Tucker +1
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 distribut…
Log-Concavity of Combinations of Sequences and Applications to Genus Distributions
Jonathan L. Gross, Toufik Mansour, Thomas W. Tucker +1
We formulate conditions on a set of log-concave sequences, under which any linear combination of those sequences is log-concave, and further, of conditions under which linear combi…
Infinite Motion and 2-Distinguishability of Graphs and Groups
Wilfried Imrich, Simon M. Smith, Thomas W. Tucker +1
A group A acting faithfully on a set X is 2-distinguishable if there is a 2-coloring of X that is not preserved by any nonidentity element of A, equivalently, if there is a proper…
Distinguishability of infinite groups and graphs
Simon M. Smith, Thomas W. Tucker, Mark E. Watkins
The {\em distinguishing number} of a group acting faithfully on a set is the least number of colors needed to color the elements of so that no non-identity element of t…