TY - GEN

T1 - Generating new graphs using Boolean operations (V and λ) on adjacency and antiadjacency matrices of graphs

AU - Putri, Gisca A.T.A.

AU - Adinegoro, Wismoyo

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}. 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84984571866&partnerID=8YFLogxK

U2 - 10.1063/1.4946905

DO - 10.1063/1.4946905

M3 - Conference contribution

AN - SCOPUS:84984571866

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 -