<p>As pointed out in comments by <a href="https://cstheory.stackexchange.com/users/129/joshua-grochow">Joshua Grochow</a>, this is a definition of <em>triangle-free graph</em>.</p>

CC BY-SA 3.0
2018-03-07T13:13:21.790Z
2018-03-07T13:13:21.790Z
aluriak
<p>I am struggling to find in literature a name for a kind of graph where all local clustering coefficients are equal to zero (or, at least, bounded).
For instance, domino, a subset of cacti and all linear graphs belong to this class. 
I do not know if such objects are named.</p>

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2018-03-02T14:28:58.370Z
If you actually want *equal* to zero, isn't this the same as being triangle-free?
Joshua Grochow
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2018-03-02T15:47:32.217Z
Is *cactii* supposed to be plular of *cactius*? There is no such word.
Emil Jeřábek
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2018-03-07T13:10:45.323Z
@Joshua: hum, yes. I forgot that expression. I answers the question with that.
aluriak
CC BY-SA 3.0
2018-03-07T13:12:10.053Z
@Emil: Well, it is used in biology and french. I did not research for equivalent in other fields or in english.
aluriak
CC BY-SA 3.0
2018-03-07T13:15:23.107Z
@aluriak No, the word used in biology etc. is *cactus*, with plural *cacti*.
Emil Jeřábek
CC BY-SA 3.0
2018-03-08T15:45:01.507Z
Oh, sorry, i did not see my additional *i*, which is a mistake. I now understand your remark. Thanks.
aluriak
<graph-theory>
What is the name of a graph with local clustering coefficients equal to zero?
aluriak
# What is the name of a graph with local clustering coefficients equal to zero?

(Asked by: username_0 on 2018-03-02)

I am struggling to find in literature a name for a kind of graph where all local clustering coefficients are equal to zero (or, at least, bounded).
For instance, domino, a subset of cacti and all linear graphs belong to this class.
I do not know if such objects are named.

**Tags:** graph-theory
> **Comments:**
> **username_1**: If you actually want *equal* to zero, isn't this the same as being triangle-free?  
> **username_2**: Is *cactii* supposed to be plular of *cactius*? There is no such word.  
> **username_0**: @Joshua: hum, yes. I forgot that expression. I answers the question with that.  
> **username_0**: @Emil: Well, it is used in biology and french. I did not research for equivalent in other fields or in english.  
> **username_2**: @aluriak No, the word used in biology etc. is *cactus*, with plural *cacti*.  
> **username_0**: Oh, sorry, i did not see my additional *i*, which is a mistake. I now understand your remark. Thanks.  

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## 1 answers

### Answer by username_0 on 2018-03-07. Score: 2 | Accepted answer

As pointed out in comments by [Joshua Grochow](https://cstheory.stackexchange.com/users/129/joshua-grochow), this is a definition of *triangle-free graph*.


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