I am currently researching divergent integrals. Definition. An extended number is an expression of the form $\int_a^b f(x)dx$, where function $f(x)$ is defined almost everywhere at $(a,b)$. Generally (when Riemann or Lebesgue sum converges or when the equivalence follows from the rules expressed...

Let $G_k$ be the graph obtained by applying the following procedure k-times: Start with a graph with single vertex $v$ (Call this graph $H$) Add a vertex $u$ such that $u$ is not adjacent to any vertex of $H$ (i.e., $K:= H \cup \{u\}$) union of two graphs Add a vertex $w$ such that $w$ is adja...

Let $G_k$ be the graph obtained by applying the following procedure k-times: Start with a graph with single vertex $v$ (Call this graph $H$) Add a vertex $u$ such that $u$ is not adjacent to any vertex of $H$ (i.e., $K:= H \cup \{u\}$) union of two graphs Add a vertex $w$ such that $w$ is adja...