Intereting Posts

What's an easy way of proving a subgroup is normal?
Associated Stirling Number of the Second Kind summation
Find $a,n\in \mathbb N^{+}:a!+\dfrac{n!}{a!}=x^2,x\in \mathbb N$
The expected area of a triangle formed by three points randomly chosen from the unit square
Generalized birthday problem (or continuous capture recapture?)
A definite integral related to Ahmed's integral
why is a nullary operation a special element, usually 0 or 1?
pseudo-primality and test of Solovay-Strassen
Rigorous book on bootstrapping, boosting, bagging, etc.
Showing $\left|\frac{a+b}{2}\right|^p+\left|\frac{a-b}{2}\right|^p\leq\frac{1}{2}|a|^p+\frac{1}{2}|b|^p$
Proofs that every natural number is a sum of four squares.
example of a continuous function that is closed but not open
How to prove $ \sin x=…(1+\frac{x}{3\pi})(1+\frac{x}{2\pi})(1+\frac{x}{\pi})x(1-\frac{x}{3\pi})(1-\frac{x}{2\pi})(1-\frac{x}{\pi})…$?
Proof of the inequality $e^x\le e^{x^2} + x$
Find $E(e^{-\Lambda}|X=1)$ where $\Lambda\sim Exp(1)$ and $P(X=x)=\frac{\lambda^xe^{-\lambda}}{x!}$.

I have just started studying graph theory and having trouble with understanding the difference b/w isomorphism and equality of two graphs.According what I have studied so far, I am able to conclude that isomorphic graphs can have same diagrams when represented on paper, but equal graphs also have same diagram on paper, if that is so, then what is the difference b/w equality and isomorphism.

It would be really helpful, if a person could throw some light on what are the difference b/w the above two terms. Specifically, any example of an isomorphic graph which is not equal.

- Reorder adjacency matrices of regular graphs so they are the same
- Non-isomorphic graphs with four total vertices, arranged by size
- Confusion about the hidden subgroup formulation of graph isomorphism
- Are these 2 graphs isomorphic?
- How to find non-isomorphic trees?

- Let $G$ be a graph of minimum degree $k>1$. Show that $G$ has a cycle of length at least $k+1$
- Pairs of points exactly $1$ unit apart in the plane
- Proof a graph is bipartite if and only if it contains no odd cycles
- Painting a cube with 3 colors (each used for 2 faces).
- Graph with 10 nodes and 26 edges must have at least 5 triangles
- Recurrence with varying coefficient
- Connection Between Automorphism Groups of a Graph and its Line Graph
- Non-isomorphic graphs with four total vertices, arranged by size
- If a graph has a Hamilton Path starting at every vertex, must it contain a Hamilton Circuit?
- Prove that a planar graph is connected if it has $p$ vertices and $3p-7$ edges

By definition a graph is a set of edges $E\subseteq V^2$ and vertices. An other graph

$\bar E\subseteq \bar V^2$ is equal if $E=\bar E$ and $V=\bar V$, but isomorphic if there exists a bijection $f:V\rightarrow \bar V$ such that

$(x,y)\in E \Rightarrow (f(x),f(y))\in \bar E$.

Isomorphic is as close as can be when the graphs not have identical sets of edges and vertices.

This two graphs are isomorphic, but not equal. In applications where the graphs are LABELLED, the useful concept might be equality and a mere isomorphism may not be enough.

Mom Dad

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Son
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Son Dad

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Mom
```

A graph is a set of vertices and edges. Isomorphic graphs *look* the same but aren’t. For example, the persons in a household can be turned into a graph by decalring that there is an edge $ab$ whenever $a$ is parent or child of $b$. So the graph of the inhabitants of a certin house in Evergreen terrace, Springfield, consists of five vertices where each of “Marge” and “Homer” is directly connected with each of “Bart”, “Lisa”, “Maggie”. We would obtain an *isomorphic* graph with any other typical couple-with-three-kids household, but not the *same* (i.e. not all these graphs will contain a vertex named Homer).

- Hairy Ball theorem and its applications
- Show that $\int_0^ \infty \frac{1}{1+x^n} dx= \frac{ \pi /n}{\sin(\pi /n)}$ , where $n$ is a positive integer.
- Total number of unordered pairs of disjoint subsets of S
- An Example for a Graph with the Quaternion Group as Automorphism Group
- injective and surjective
- Why are harmonic functions called harmonic functions?
- Finding the limit $\lim_{n\rightarrow\infty}(1-\frac{1}{3})^2(1-\frac{1}{6})^2(1-\frac{1}{10})^2…(1-\frac{1}{n(n+1)/2})^2$
- Does this sequence always give a square number?
- Bounded random walk on one side only: Are you guaranteed to hit the bound?
- How to evaluate $\int_0^1 \frac{\ln(x+1)}{x^2+1} dx$
- Why is a set of orthonormal vectors linearly independent?
- (combinatorics) prove that on average, n-permutations have Hn cycles without mathematical induction.
- Solving second order nonlinear ODE
- Help me prove this inequality :
- An application of the General Lebesgue Dominated convergence theorem