The Scrambling Index And Generalized Scrambling Index Of Two Types Of Primitive Digraph

Combinatorial mathematics is also known as discrete mathematics. It is a discipline ofstudying the presence of discrete structures, counting, analysis and optimization problems.Combinatorial mathematics has extremely important place, not only in basic mathematicsresearch, but also in other disciplines such as coding and cryptography, computer science,chemistry, physics, biology and other disciplines, even in urban logistics, transport planning,directing a war, business management, financial analysis. The scrambling index of primitivedigraphs has become one of the emerging research focuses in combinatorial mathematics.This paper mainly studies the scrambling index of a class of primitive digraph with differentcycles and the scrambling index of a special class of primitive digraph. The main content is asfollows：Chapter I gives an overview of the history and significance of the combinatorialmathematics and graph theory, and explains the related concepts of the primitive digraph,primitive index and scrambling index on this basis,at the same time, which gives the mainconclusions of this paper.Chapter II primarily studies two types of the special primitive digraphs. The indeed valueof the scrambling index are separately obtained.Chapter III discusses the above two types of order n of the special primitive digraphs indetail, and gives the indeed value of theλth lowerμ-scrambling index and the upper boundof theλth upperμ-scrambling index.