TY - GEN

T1 - Comparing the largest eigenvalue on adjacency and antiadjacency matrices of graphs which constructed using Boolean operation (⊕ and ⊕)

AU - Adinegoro, Wismoyo

AU - Putri, Gisca A.T.A.

AU - Ariyanti, Kiki

PY - 2016/4/19

Y1 - 2016/4/19

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84984572871&partnerID=8YFLogxK

U2 - 10.1063/1.4946908

DO - 10.1063/1.4946908

M3 - Conference contribution

AN - SCOPUS:84984572871

T3 - AIP Conference Proceedings

BT - International Symposium on Current Progress in Mathematics and Sciences 2015, ISCPMS 2015

A2 - Mart, Terry

A2 - Triyono, Djoko

PB - American Institute of Physics Inc.

T2 - 1st International Symposium on Current Progress in Mathematics and Sciences, ISCPMS 2015

Y2 - 3 November 2015 through 4 November 2015

ER -