Get Zero-symmetric Graphs: Trivalent Graphical Regular PDF

By H. S. M. Coxeter

ISBN-10: 0121945804

ISBN-13: 9780121945800

Zero-Symmetric Graphs: Trivalent Graphical normal Representations of teams describes the zero-symmetric graphs with no more than one hundred twenty vertices.The graphs thought of during this textual content are finite, hooked up, vertex-transitive and trivalent.

This booklet is prepared into 3 components encompassing 25 chapters. the 1st half stories the various periods of zero-symmetric graphs, based on the variety of primarily diversified edges incident at each one vertex, particularly, the S, T, and Z periods. the remainder components speak about the theory and features of kind 1Z and 3Z graphs. those components discover Cayley graphs of particular teams, together with the parameters of Cayley graphs of groups.

This ebook will end up beneficial to mathematicians, desktop scientists, and researchers.

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Get Zero-symmetric Graphs: Trivalent Graphical Regular PDF

Zero-Symmetric Graphs: Trivalent Graphical commonplace Representations of teams describes the zero-symmetric graphs with no more than one hundred twenty vertices. The graphs thought of during this textual content are finite, hooked up, vertex-transitive and trivalent. This ebook is geared up into 3 components encompassing 25 chapters.

Additional resources for Zero-symmetric Graphs: Trivalent Graphical Regular Representations of Groups

Sample text

By By analogy with with Section Section 6, 6, we we may may call call this this graph graph t{4,4}b,c· t{4,4}t ) . 9) bk + cc E 0 0 (mod (mod m) m) .. ) It be pointed pointed out, It should should be out, however, however, that that such such aa solution solution may may fail fail to to exist; exist; within within the the range range of of values values considered considered in this this study study (m (m <<_ 30) 30) this this happens happens only only once, once, namely namely if if in b = 4, 4, c c = = 2 .

Order 2rnn 2mn Order m m nn kk gg O-symmetric? 0-symmetric? 11 42 42 77 33 3,5 3,5 66 no no 22 54 54 99 33 2,5 2,5 66 yes yes 33 44 60 60 55 13 13 66 2,3 2,3 99 yes yes 33 14 14 33 4,10 4,10 3,5 3,5 66 66 no no yes yes 10 10 yes yes 55 66 78 78 84 84 100 100 108 108 55 10 10 2,3 2,3 18 18 yes yes 11 11 33 55 66 110 110 2,6 2,6 10 10 yes yes 8B 8B 110 110 11 11 55 7,8 7,8 10 10 no no 99 114 114 120 120 19 19 33 10 10 66 8,12 8,12 3,7 3,7 77 8A 8A 10 10 41 41 . 1 aa column column with with the the value value of of g.

For For this this purpose purpose let let us us consider separately separately the the cases cases of of odd odd and and even even values values of of m. m. consider It It can can be be seen seen from from the the Cayley Cayley diagram diagram (Fig. (Fig. 1) that that 1 -1 i the R) corresponds corresponds to to aa path path leading, leading, for for the word word (SRS (SRS "*"R) instance, from from the the vertex vertex "0" " 0 " to to that that labeled labeled 4i(k+l), 4i(k+l), and and instance, this is is an an open open path path for for this = I, 1/ 2, 2, 3, 3, ...

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Zero-symmetric Graphs: Trivalent Graphical Regular Representations of Groups by H. S. M. Coxeter


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