general
Self complementary graph with a pendant vertex
Show that if a self-complementary graph contains a pendant vertex, then it must have at least another pendant vertex. Let $G$ be a graph of order $n$, so ...
Apr 17, 2026
Archive: General
general
A more succinct definition of subfield
I'm reading textbook Algebra by Saunders MacLane and Garrett Birkhoff in which a subfield is defined as A subset of a field $F$ is a subfield if and ...
Apr 17, 2026
general
How to show $f$ is one one and onto by the concept of graph.
Let $f :\mathbb R \to \mathbb R$ be a function. Then Show that $f$ is one one if the graph of $f$ intersects any line parallel to the $X$ - axis in at mos...
Apr 17, 2026
general
Proportional Image Resizing
This is quite a simple one I guess (but my mind is dead currently and is getting cluttered by other numbers). I have an square image that is currently 256...
Apr 17, 2026
general
Zeros of Bessel functions
Let $J_\nu(x):=\displaystyle\sum^\infty_{k=0}\frac{(-1)^k(x/2)^{\nu+2k}}{k!~\Gamma(\nu+k+1)}$ denote a Bessel function. When $\nu\geq0$, let $0<j_{\nu,...
Apr 17, 2026
general
Is a homomorphisim one-to-one or onto?
The definition of a homomorphism $f$ from $G$ to $H$, given by Pinter, says that: If $G$ and $H$ are groups, a homomorphism from $G$ to $H$ is a function ...
Apr 17, 2026
general
Edges on an even number of Hamilton cycles
Let $G$ be a graph in which every vertex has odd degree. Show that every edge of $G$ lies on an even number of Hamilton cycles.
Apr 17, 2026
general
In MATLAB, $\pi$ value is given as 355/113. why?
$\pi$ is an irrational number. MATLAB shows it equal to 355/113 in fractional format. Is there no better fractional representation than 355/113 within the...
Apr 17, 2026
general
Solving the matrix differential equation $v'(z) = A e^z + B v(z), v'(0) = 0)$
Take the system of ODEs in terms of the scalar $z$, $$v'(z) = A e^z + B\cdot v(z)$$ With the initial condition, $$v'(0) = \mathbf{0}$$ For some ...
Apr 17, 2026
general
Let $(x_n)$ be a bounded but not convergent sequence. Prove that $(x_n)$ has two subsequences converging to different limits.
Let $(x_n)$ be a bounded but not convergent sequence. Prove that $(x_n)$ has two subsequences converging to different limits. My attempt is: Since the seq...
Apr 16, 2026
