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Dec
10
awarded  Caucus
Nov
27
comment Why this graph has automorphism group is isomorphic to the cyclic group of order 4?
@HenningMakholm If $\phi$ carries $v_1$ to $v_2$ where $v_i$'s are vertices with degree 5, then $\phi$ should carry $u_1$ to $u_2$ where $u_i$ is nbhd of $v_i$ with degree 2. We can use this fact for determining $\phi$. Is it clear?
Nov
27
comment Why this graph has automorphism group is isomorphic to the cyclic group of order 4?
each vertex of degree 5 has exactly one nhbd with vertex 2 so if $\phi$ fixes vertices with degree 5, then $\phi$ fixes vertices with degree 2. Now, since each vertex of degree 2 has exactly one nhbd with vertex 3 so if \phi fixes vertices with degree 2, then \phi fixes vertices with degree 3. Thus \phi fixes all vertices. Is it clear?
Nov
27
revised Why this graph has automorphism group is isomorphic to the cyclic group of order 4?
edited body
Nov
27
comment Why this graph has automorphism group is isomorphic to the cyclic group of order 4?
@ChrisGodsil, thanks.
Nov
27
revised Why this graph has automorphism group is isomorphic to the cyclic group of order 4?
deleted 11 characters in body
Nov
27
revised Why this graph has automorphism group is isomorphic to the cyclic group of order 4?
added 9 characters in body
Nov
27
comment Why this graph has automorphism group is isomorphic to the cyclic group of order 4?
Note that there are only two groups with order $4$($\mathbb Z_2\times\mathbb Z_2$ and $\mathbb Z_4$).
Nov
27
answered Why this graph has automorphism group is isomorphic to the cyclic group of order 4?
Nov
25
comment Graph with only the identity as endomorphism
For infinite case, see Graphs with given infinite group by Sabidussi.There are infinitely many asymmetric cubic graphs.
Nov
24
comment how we can understand from spectrum of laplacian matrix of a graph that this graph is regular or not .
No, problem. It is ok.
Nov
24
answered prove that we can calculate $\sum^n_{i=1} d^{2}_{i}$ from the spectrum of laplacian matrix of graph.
Nov
24
comment how we can understand from spectrum of laplacian matrix of a graph that this graph is regular or not .
khahesh mikonam che jaleb man fkr mikardam shoma Romanian hastid.
Nov
24
comment how we can understand from spectrum of laplacian matrix of a graph that this graph is regular or not .
@kpax your welcome. May be this paper helps you:Which graphs are determined by their spectrum? by Dam and Haemers.
Nov
24
answered how we can understand from spectrum of laplacian matrix of a graph that this graph is regular or not .
Nov
24
reviewed Reject How to determine whether the following sets are countable:
Nov
24
reviewed Approve Simple problem about Laplace Equation in a domain
Nov
20
awarded  Enlightened
Nov
20
awarded  Nice Answer
Nov
20
comment The limit of $\tan(n)$
I like your proof.