Characteristic polynomial of anti-Adjacency matrix of directed cyclic friendship graph

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Abstract

Graph theory has some applications. One of them is used to do social network analysis as in Facebook with each person as nodes and every like, share, comment, tag as edges. Usually a network can be represented by a graph. Analysing a network is the same as analysing the structure of a graph. A structure of a graph can be analysed through some matrix representations such as anti-Adjacency matrix. The entries of the anti-Adjacency matrix of a directed graph represent the presence or absence of directed arcs from a vertex to the others. This paper is about the properties of the anti-Adjacency matrix of directed cyclic friendship graph, those are the characteristic polynomial and the eigenvalues of the anti-Adjacency matrix. The method used to obtain the general form of the coefficients of the characteristic polynomial is by adding up the determinant values of all directed induced subgraphs, cyclic or acyclic, of the directed cyclic friendship graph. Furthermore, the methods used to find theeigenvalues of the anti-Adjacency matrix of directed cyclic friendship graph are the substitution method and factorization method. The result of this researcharethe general form of the coefficients of the characteristic polynomial and the general form of the eigenvalues of the anti-Adjacency matrix depend on the number of triangles in directed cyclic friendship graph.

Original languageEnglish
Article number012007
JournalJournal of Physics: Conference Series
Volume1538
Issue number1
DOIs
Publication statusPublished - 19 Jun 2020
Event3rd International Conference on Combinatorics, Graph Theory, and Network Topology, ICCGANT 2019 - East Java, Indonesia
Duration: 26 Oct 201927 Oct 2019

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