• 1
Book
...The nine finite, planar, 3-connected, edge-transitive graphs have been known and studied for many centuries. The infinite, locally finite, planar, 3-connected,...

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Book
...Combinatorics and graph theory have mushroomed in recent years. Many overlapping or equivalent results have been produced. Some of these are special cases of...
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Journal Article
...A Frobenius group is a transitive permutation group that is not regular and such that only the identity fixes more than one point. A graphical Frobenius...

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Book

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Journal Article
...A tessellation is understood to be a 1-ended, locally finite, 3-connected planar map. The edge-symbol $\langle p,q;k,\ell\rangle$ of an edge of a tessellation...
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Journal Article
...A graphical Frobenius representation (GFR) of a Frobenius (permutation) group $G$ is a graph $\Gamma$ whose automorphism group Aut$(\Gamma)$ acts as a...
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eBook
...Passage to Abstract Mathematics helps students progress from a facility with computational procedures to an understanding of abstract mathematical concepts...
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Journal Article
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Journal Article
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Journal Article
...A group of permutations $G$ of a set $V$ is $k$-distinguishable if there exists a partition of $V$ into $k$ cells such that only the identity permutation in...
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Journal Article
...A group $$A$$ A acting faithfully on a set $$X$$ X is $$2$$ 2 -distinguishable if there is a $$2$$ 2 -coloring of $$X$$ X that is not preserved by any...

• 12
Journal Article
...The distinguishing number of a group $G$ acting faithfully on a set $V$ is the least number of colors needed to color the elements of $V$ so that no...
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Journal Article
...The distinguishing number $\Delta(X)$ of a graph $X$ is the least positive integer $n$ for which there exists a function $f:V(X)\to\{0,1,2,\cdots,n-1\}$ such...
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Journal Article
...Byline: Wilfried Imrich (1), Simon M. Smith (2), Thomas W. Tucker (3), Mark E. Watkins (4) Author Affiliation: (1) Montanuniversitat Leoben, 8700, Leoben,...

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Journal Article
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Journal Article
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Journal Article
• 18
Journal
...The distinguishing number of a group G acting faithfully on a set V is the least number of colors needed to color the elements of V so that no non-identity...
• 19
Journal Article
...We present a theory of Cayley maps, i.e., embeddings of Cayley graphs into oriented surfaces having the same cyclic rotation of generators around each vertex...

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Journal Article
by Graver, Jack E   Watkins, Mark E
29.11.2018
...We give necessary and sufficient conditions for lobe-transitivity of locally finite and locally countable graphs whose connectivity equals 1. We show further...