‎Metric dimension and defensive $k$-alliance number are two distance-based graph invariants‎ ‎which have applications in robot navigation‎, ‎quantitative analysis of secondary RNA structures‎, ‎national defense and ...

‎We define a refinement of the notion of Leray simplicial complexes and study its properties‎. ‎Moreover‎, ‎we translate some of our results to the language of commutative algebra‎.

For a graph $G=(V,E)$, a set $S subseteq V$ is a $[1,2]$-set if it is a dominating set for $G$ and each vertex $v in V setminus S$ is dominated by at most two vertices of $S$, i.e. $1 leq vert N(v) cap S vert leq 2$. ...

Let $R$ be a ring and $alpha$ be a ring endomorphism of $R$‎. ‎The undirected nilpotent graph of $R$‎, ‎denoted by $Gamma_N(R)$‎, ‎is a graph with vertex set $Z_N(R)^*$‎, ‎and two distinct vertices $x$ and $y$ are connected ...

In this paper we classify distance-regular graphs‎, ‎including strongly regular graphs‎, ‎admitting a transitive action of the linear groups $L(3,2)$‎, ‎$L(3,3)$‎, ‎$L(3,4)$ and $L(3,5)$ for which the rank of the permutation ...