Timeline for Lower bound on the individualization set for $k$-iso-regular graphs ( degree at max three )?
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| Sep 21, 2017 at 13:05 | comment | added | Brendan McKay | The set $\lbrace 4,5\rbrace$ and the set $\lbrace 4,14\rbrace$ both induce an empty subgraph. But 4,5 have one common neighbour and 4,14 have none. So your graph isn't $k$-isoregular for $k\ge 2$. Actually, as Aaron says, 2-isoregular is the same as strongly regular. | |
| Sep 21, 2017 at 9:11 | comment | added | fddwd | @Brendan McKay I have edited the question and given the definition of $k$-iso-regular. | |
| Sep 21, 2017 at 9:10 | history | edited | fddwd | CC BY-SA 3.0 |
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| Sep 21, 2017 at 8:56 | comment | added | Brendan McKay | I down-voted. Several days after Aaron told your that your definition of $k$-iso-regular makes no sense, you still didn't fix it. Under your definition, every graph is $k$-iso-regular when $k$ is greater than the maximum degree, and it is not true that $k$-iso-regular implies $k-1$-iso-regular. I'll also note that the definition in Douglas' paper is different from the definition in his reference [11] that he claims to get it from. | |
| Sep 21, 2017 at 1:37 | review | Close votes | |||
| Sep 22, 2017 at 0:54 | |||||
| Sep 20, 2017 at 14:09 | history | edited | fddwd | CC BY-SA 3.0 |
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| Sep 17, 2017 at 16:58 | answer | added | Aaron Meyerowitz | timeline score: 1 | |
| Sep 17, 2017 at 13:41 | history | edited | fddwd | CC BY-SA 3.0 |
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| Sep 17, 2017 at 13:31 | history | edited | fddwd | CC BY-SA 3.0 |
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| Sep 17, 2017 at 13:29 | comment | added | fddwd | @ Brendan McKay This is 4-iso-regular | |
| Sep 17, 2017 at 13:17 | comment | added | Brendan McKay | The example seems to be 1-iso-regular but not 2-iso-regular. Otherwise I don't understand the definition. Please give a non-trivial example of a 2-iso-regular graph with maximum degree 3. Frankly I am doubting their existence (except for some tiny graphs). | |
| Sep 17, 2017 at 12:59 | history | edited | fddwd | CC BY-SA 3.0 |
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| Sep 17, 2017 at 12:42 | history | edited | fddwd | CC BY-SA 3.0 |
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| Sep 17, 2017 at 12:15 | comment | added | fddwd | @ Brendan McKay It is not just number of neighbours, but number of common neighbours. I have edited the question | |
| Sep 17, 2017 at 12:14 | history | edited | fddwd | CC BY-SA 3.0 |
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| Sep 17, 2017 at 10:35 | comment | added | Brendan McKay | How is the number of neighbours of a $k$-tuple defined? | |
| Sep 17, 2017 at 10:06 | history | edited | fddwd | CC BY-SA 3.0 |
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| Sep 17, 2017 at 9:52 | history | edited | fddwd | CC BY-SA 3.0 |
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| Sep 17, 2017 at 9:34 | history | edited | fddwd | CC BY-SA 3.0 |
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| Sep 17, 2017 at 9:23 | history | asked | fddwd | CC BY-SA 3.0 |