We establish the tracial stability of a certain class graph products C*-algebras. This result involves development pincushion finite graphs. then apply this in two ways. The first application yields selective version Lin's Theorem for almost commuting operators. second addresses some approximation properties right-angled Artin groups. In particular, we show that full C*-algebra any group is qua...

Foucaud, Krishna and Ramasubramony Sulochana recently introduced the concept of monitoring edge-geodetic sets in graphs, a related graph invariant. These are vertices such that removal any edge changes distance between some pair set. They studied minimum possible size set given graph, which we call number. We show decision problem for number is NP-complete. also give best-possible upper lower b...

A defensive alliance in a graph is a set $S$ of vertices with the property that every vertex in $S$ has at most one moreneighbor outside of $S$ than it has inside of $S$. A defensive alliance $S$ is called global if it forms a dominating set. The global defensive alliance number of a graph $G$ is the minimum cardinality of a global defensive alliance in $G$. In this article we study the global ...

We define the type of graph products, which enable us to treat many graph products in a unified manner. These unified graph products are shown to be compatible with Godsil–McKay switching. Furthermore, by this compatibility, we show that the Doob graphs can also be obtained from the Hamming graphs by switching.