TY - JOUR
T1 - A Comparative Study of Three Resolving Parameters of Graphs
AU - Ikhlaq, Hafiz Muhammad
AU - Siddiqui, Hafiz Muhammad Afzal
AU - Imran, Muhammad
N1 - Publisher Copyright:
© 2021 Hafiz Muhammad Ikhlaq et al.
PY - 2021
Y1 - 2021
N2 - Graph theory is one of those subjects that is a vital part of the digital world. It is used to monitor the movement of robots on a network, to debug computer networks, to develop algorithms, and to analyze the structural properties of chemical structures, among other things. It is also useful in airplane scheduling and the study of diffusion mechanisms. The parameters computed in this article are very useful in pattern recognition and image processing. A number df,w=mindw,t,dw,s is referred as distance between f=ts an edge and w a vertex. dw,f1≠dw,f2 implies that two edges f1,f2∈E are resolved by node w∈V. A set of nodes A is referred to as an edge metric generator if every two links/edges of Γ are resolved by some nodes of A and least cardinality of such sets is termed as edge metric dimension, edimΓ for a graph Γ. A set B of some nodes of Γ is a mixed metric generator if any two members of V∪E are resolved by some members of B. Such a set B with least cardinality is termed as mixed metric dimension, mdimΓ. In this paper, the metric dimension, edge metric dimension, and mixed metric dimension of dragon graph Tn,m, line graph of dragon graph LTn,m, paraline graph of dragon graph LSTn,m, and line graph of line graph of dragon graph LLTn,m have been computed. It is shown that these parameters are constant, and a comparative analysis is also given for the said families of graphs.
AB - Graph theory is one of those subjects that is a vital part of the digital world. It is used to monitor the movement of robots on a network, to debug computer networks, to develop algorithms, and to analyze the structural properties of chemical structures, among other things. It is also useful in airplane scheduling and the study of diffusion mechanisms. The parameters computed in this article are very useful in pattern recognition and image processing. A number df,w=mindw,t,dw,s is referred as distance between f=ts an edge and w a vertex. dw,f1≠dw,f2 implies that two edges f1,f2∈E are resolved by node w∈V. A set of nodes A is referred to as an edge metric generator if every two links/edges of Γ are resolved by some nodes of A and least cardinality of such sets is termed as edge metric dimension, edimΓ for a graph Γ. A set B of some nodes of Γ is a mixed metric generator if any two members of V∪E are resolved by some members of B. Such a set B with least cardinality is termed as mixed metric dimension, mdimΓ. In this paper, the metric dimension, edge metric dimension, and mixed metric dimension of dragon graph Tn,m, line graph of dragon graph LTn,m, paraline graph of dragon graph LSTn,m, and line graph of line graph of dragon graph LLTn,m have been computed. It is shown that these parameters are constant, and a comparative analysis is also given for the said families of graphs.
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U2 - 10.1155/2021/1927181
DO - 10.1155/2021/1927181
M3 - Article
AN - SCOPUS:85122385555
SN - 1076-2787
VL - 2021
JO - Complexity
JF - Complexity
M1 - 1927181
ER -