Generating new graphs using Boolean operations (V and λ) on adjacency and antiadjacency matrices of graphs

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

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

Abstract

Let G be a graph with V(G) = {v1, ., vn} and E(G) = {e1, ., em}. We only consider graphs with no multiple edges in this paper. The adjacency matrix of G, denoted by A(G), is the n × n matrix A = [aij], where aij = 1 if e = vi vj ϵ E(G) or aij = 0 otherwise. The antiadjacency matrix of G, denoted by B(G), is the n × n matrix B = [bij], where bij = 0 if e = vi vj ϵ E(G) or bij = 1 otherwise. Harary and Wilcox have considered Boolean operations on two graphs G1 and G2, resulting a new graph G whose V(G) equals V(G1) × V(G2). On this paper, Boolean operations are defined for two adjacency and two antiadjacency matrices of graphs Gl and G2 with V(G1) = V(G2) rather than looking at the two graphs themselves. Boolean operations which are reviewed on this paper are V and λ. The objectives of this paper are to introduce the operations on two adjacency or two antiadjacency matrices of graph G, to discover some characteristics of the operations on the matrices, to construct a new graph which is generated using the operators on two adjacency or antiadjacency matrices, and to reveal the similarity between operators on adjacency matrix and operators on antiadjacency matrix based on the represented graph. This paper also emphasizes on investigating the relationship between the operators and on comparing the largest eigenvalue between graphs which are constructed by Boolean operators on both adjacency and antiadjacency matrices.

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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