The present work aims to present a study on the Theory of Graphs, as well as to present
some of its applications seeking to articulate the concepts of Graphs to the knowledge of
Linear Algebra. To this end, we seek to highlight the characteristics of different types of
graphs, their structure and main definitions. We willshow the first theorem established by the
mathematician Leonard Euler when solving the problem of Konigsberg bridges and some
applications used in games. We will present ways of representing graphs by means of
specific matrices, giving more emphasis to the adjacency matrix and Laplacian matrix,
which we will approach some of their properties, especially the characteristic polynomial,
eigenvalues and eigenvectors, as well as a study of their respective specters. An
application in the field of Chemistry will be presented, which seeks to discover the presence
or absence of quaternary carbon in a given molecule under study
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