Properties of characteristic polynomial and eigenvalues of antiadjacency matrix of directed unicyclic tadpole graph

Qomaruzzaman, S. Aminah, K. A. Sugeng

Research output: Contribution to journalConference articlepeer-review

Abstract

A directed cyclic graph is a directed graph that has at least one directed cycle graph, that is a cycle graph in which all edges are oriented, so that the direction passes through each vertex once, except the end of vertex. The directed unicyclic tadpole graph Tm, n is the graph created by concatenating a cycle Cm and a path Pn with an edge from any vertex of Cm to a pendant of Pn for integers m = 3 and n = 1. Antiadjacency matrix is a directed graph representation matrix based on whether or not there is a relation between one vertex and the others. This paper gives the general form of coefficients of characteristic polynomial and eigenvalues of antiadjacency matrix of directed unicyclic tadpole graph. To find the general form of coefficients of characteristic polynomial and eigenvalues of antiadjacency matrix of directed unicyclic tadpole graph we need to do the grouping of induced subgraphs into acyclic and cyclic and verify with related theorems. After that, the characteristic polynomial is factorized and the roots are calculatedto find its eigenvalues. The coefficients of the characteristic polynomial consist of three distinct values and the eigenvalues are divided into odd case and even case.

Original language English 012002 Journal of Physics: Conference Series 1836 1 https://doi.org/10.1088/1742-6596/1836/1/012002 Published - 23 Mar 2021 Yes 4th International Conference on Combinatorics, Graph Theory, and Network Topology, ICCGANT 2020 - Jember, East Java, IndonesiaDuration: 22 Aug 2020 → 23 Aug 2020

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