Comparing the largest eigenvalue on adjacency and antiadjacency matrices of graphs which constructed using Boolean operation (⊕ and ⊕)

Wismoyo Adinegoro, Gisca A.T.A. Putri, Kiki Ariyanti

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Citation (Scopus)

Abstract

Let G be a graph with V(G) = {v1, ., vn} and E(G) = {e1, ., em}. In this paper, only graphs with no multiple edges are observed. The n × n matrix A = [aij], where aij = 1 if e = vi vj ϵ E(G) and aij = 0 otherwise, is the adjacency matrix of G and is denoted by A(G). The n × n matrix B = [bij], where bij = 0 if e = vi vj ϵ E(G) and bij = 1 otherwise, is the antiadjacency matrix of G and is denoted by B(G). Boolean operations on two graphs have been examined by Harary and Wilcox. Hence, this paper will consider Boolean operations on two adjancency and antiadjancency matrices of two graphs G1 and G2 with V(G1) = V(G2). Boolean operations which are reviewed on this paper are OR (V), AND (λ), XOR(⊕), and NXOR(⊕) However, the paper only focus on operation ⊕ and ⊕. The purposes of this paper are to introduce the operations on two adjacency and antiadjacency matrices of two graphs G1 and G2 with V(G1) = V(G2), to reveal the effect on the represented graph using operations ⊕ and ⊕ on both adjacency and antiadjacency matrices, and to compare the largest eigenvalues between the matrices generated by the Boolean operations.

Original languageEnglish
Title of host publicationInternational Symposium on Current Progress in Mathematics and Sciences 2015, ISCPMS 2015
Subtitle of host publicationProceedings of the 1st International Symposium on Current Progress in Mathematics and Sciences
EditorsTerry Mart, Djoko Triyono
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735413764
DOIs
Publication statusPublished - 19 Apr 2016
Event1st International Symposium on Current Progress in Mathematics and Sciences, ISCPMS 2015 - Depok, Indonesia
Duration: 3 Nov 20154 Nov 2015

Publication series

NameAIP Conference Proceedings
Volume1729
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference1st International Symposium on Current Progress in Mathematics and Sciences, ISCPMS 2015
CountryIndonesia
CityDepok
Period3/11/154/11/15

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