We prove that the graph obtained from the non-nilpotent graph of a finite group by deleting the isolated vertices is connected with diameter at most 3‎. ‎This bound is the best possible‎.

The zero forcing number $Z(G)$ of a graph $G$ is the minimum cardinality of a set $S$ with colored (black) vertices which forces the set $V(G)$ to be colored (black) after some times. ``color change rule'': a white vertex ...

In this paper‎, ‎we evaluate determinants of some families of Toeplitz--Hessenberg matrices having tribonacci number entries‎. ‎These determinant formulas may also be expressed equivalently as identities that involve sums ...

‎Let $x$ be a vertex of a connected graph $G$ and $W subset V(G)$ such that $xnotin W$‎. ‎Then $W$ is called an $x$-Steiner set of textit{G} if $W cup lbrace x rbrace$ is a Steiner set of textit{G}‎. ‎The minimum cardinality ...

Let $H$ be a digraph possibly with loops and $D$ a digraph without loops whose arcs are colored with the vertices of $H$ ($D$ is said to be an $H$-colored digraph)‎. ‎A directed walk $W$ in $D$ is said to be an $H$-walk ...