On very strongly perfect Cartesian product graphs

Abstract

<abstract><p>Let $ G_1 \square G_2 $ be the Cartesian product of simple, connected and finite graphs $ G_1 $ and $ G_2 $. We give necessary and sufficient conditions for the Cartesian product of graphs to be very strongly perfect. Further, we introduce and characterize the co-strongly perfect graph. The very strongly perfect graph is implemented in the real-time application of a wireless sensor network to optimize the set of master nodes to communicate and control nodes placed in the field.</p></abstract>

Prime Spectrum Graph of C-Lattices

“…According to I. Beck, the zero-divisor graph of a commutative ring is a graph where the vertices represent the elements of the ring, and two vertices are connected by an edge if their product is zero (see [5]). Further, by employing these graph-theoretic approach, many researchers visually represented and analyzed various aspects of commutative rings, providing additional insights into their structure, properties, and relationships (see [1]- [4], [9]- [10], [12]).…”