Graph theory is one of the most relevant and fastest growing branches of mathematics. Owing to its exponential growth in the past few decades and its extensive applications in diverse fields, Graph theory has become the foundation stone of applied mathematics. The book successfully employs vertex cover polynomials to determine the total domination polynomials of some graphs. It is known that the problem of finding total dominating sets in simple graphs can be translated to the concept of vertex covers in hypergraphs. This prompted us to study total domination polynomials using vertex cover...
Graph theory is one of the most relevant and fastest growing branches of mathematics. Owing to its exponential growth in the past few decades and its ...
In an era where network reliability is paramount, this work introduces a novel approach to fault-tolerant system design through the lens of graph theory. The book presents the innovative concept of "closely-connected vertices," a powerful framework that revolutionizes our understanding of network resilience and fault tolerance. Through meticulous analysis of cc-domination, graph polynomials, and entropy measures, readers will discover new methodologies for designing robust networks that minimize link failures. This comprehensive study bridges theoretical mathematics and practical...
In an era where network reliability is paramount, this work introduces a novel approach to fault-tolerant system design through the lens of graph theo...
