A Study on Development of Theory on Algebra | Original Article

ABSTRACT:

Graph Theory on Algebra is a newly emerging discipline in mathematics that has significant applications. Newline Newline In recent decades, newline complex graphical theory of algebraic structures is being increasingly used in algebraic techniques. A newline with the interplay between algebra and the theory of graphics is a fascinating topic. Algebraic tools can be used to provide surprising newline and fine evidence of theoretical graphic facts, and numerous newline graphs are linked to interesting algebraic objects. The literature itself has grown dramatically in the field of algebraic graph theory. New line Thousands of research papers was literally published. There are currently several newline books dealing with this topic. Algebraic graph theory is a branch of newline mathematics which is used for graphic problem by algebraic methods. This contrasts with the combined or algorithmic approaches of geometry and newline. The newline graphic theory has three main branches the use of linear algebra, the use of group theory and the investigation of newline graphic invariants. Newline The first branch of the graphic theory of algebraics involves a newline study of graphs with linear algebra. It studies the adjacence matrix or the newline in particular A graph's laplacian matrix (this part of algebraic graph theory is also called spectral graph newline theory). Newline The second branch of algebraic graph theory involves the investigation of graphs into group theory in connection with newline, especially auto-orophytic groups and geometric group theory. This new feature this category covers the dissertation. Newline Finally, the third branch of algebraic graph theory deals with algebraic characteristics of newline graph invariants, and particularly the chromatic polynomials of the polynomial and the nodes of newlines. The newline number counts its proper peak colours, for example, in the chromatic polynomial of a diagram.