What connected graphs are with equal vertex-connectivity and minimum degree?

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Let $G$ be a connected graph with equal vertex connectivity and minimum degree. What can we say about $G$? I am trying to find some literature about this question, but I was not able to. I will appreciate for your comments.



Thanks




graph-theory graph-connectivity




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  • 1




    An $n-$cycle will have be $2-$connected and vertex degree $2$.
    – Donald Splutterwit
    Jul 31 at 23:00










  • This might be more interesting if we talk about d-regular graphs.
    – Bob Krueger
    Aug 1 at 20:17










  • That might be a good initiator to find some characterization.
    – kswim
    Aug 1 at 22:05














up vote
0
down vote

favorite












Let $G$ be a connected graph with equal vertex connectivity and minimum degree. What can we say about $G$? I am trying to find some literature about this question, but I was not able to. I will appreciate for your comments.



Thanks




graph-theory graph-connectivity




share|cite|improve this question















  • 1




    An $n-$cycle will have be $2-$connected and vertex degree $2$.
    – Donald Splutterwit
    Jul 31 at 23:00










  • This might be more interesting if we talk about d-regular graphs.
    – Bob Krueger
    Aug 1 at 20:17










  • That might be a good initiator to find some characterization.
    – kswim
    Aug 1 at 22:05












up vote
0
down vote

favorite









up vote
0
down vote

favorite











Let $G$ be a connected graph with equal vertex connectivity and minimum degree. What can we say about $G$? I am trying to find some literature about this question, but I was not able to. I will appreciate for your comments.



Thanks




graph-theory graph-connectivity




share|cite|improve this question











Let $G$ be a connected graph with equal vertex connectivity and minimum degree. What can we say about $G$? I am trying to find some literature about this question, but I was not able to. I will appreciate for your comments.



Thanks





graph-theory graph-connectivity





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Jul 31 at 22:44









kswim

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  • 1




    An $n-$cycle will have be $2-$connected and vertex degree $2$.
    – Donald Splutterwit
    Jul 31 at 23:00










  • This might be more interesting if we talk about d-regular graphs.
    – Bob Krueger
    Aug 1 at 20:17










  • That might be a good initiator to find some characterization.
    – kswim
    Aug 1 at 22:05












  • 1




    An $n-$cycle will have be $2-$connected and vertex degree $2$.
    – Donald Splutterwit
    Jul 31 at 23:00










  • This might be more interesting if we talk about d-regular graphs.
    – Bob Krueger
    Aug 1 at 20:17










  • That might be a good initiator to find some characterization.
    – kswim
    Aug 1 at 22:05







1




1




An $n-$cycle will have be $2-$connected and vertex degree $2$.
– Donald Splutterwit
Jul 31 at 23:00




An $n-$cycle will have be $2-$connected and vertex degree $2$.
– Donald Splutterwit
Jul 31 at 23:00












This might be more interesting if we talk about d-regular graphs.
– Bob Krueger
Aug 1 at 20:17




This might be more interesting if we talk about d-regular graphs.
– Bob Krueger
Aug 1 at 20:17












That might be a good initiator to find some characterization.
– kswim
Aug 1 at 22:05




That might be a good initiator to find some characterization.
– kswim
Aug 1 at 22:05















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