TY - JOUR

T1 - Local multiset dimension of corona product on tree graphs

AU - Alfarisi, Ridho

AU - Susilowati, Liliek

AU - Dafik,

AU - Kristiana, Arika Indah

N1 - Publisher Copyright:
© 2023 World Scientific Publishing Company.

PY - 2023

Y1 - 2023

N2 - One of the topics of distance in graphs is resolving set problem. This topic has many applications in science and technology namely navigation robots, chemistry structure, and computer sciences. Suppose the set W = {s1,s2,...,sk}⊂ V (G), the vertex representations of x V (G) is rm(x|W) = {d(x,s1),d(x,s2),...,d(x,sk)}, where d(x,si) is the length of the shortest path of the vertex x and the vertex in W together with their multiplicity. The set W is called a local m-resolving set of graphs G if rm(v|W)≠rm(u|W) for uv E(G). The local m-resolving set having minimum cardinality is called the local multiset basis and its cardinality is called the local multiset dimension of G, denoted by mdl(G). In our paper, we determine the establish bounds of local multiset dimension of graph resulting corona product of tree graphs.

AB - One of the topics of distance in graphs is resolving set problem. This topic has many applications in science and technology namely navigation robots, chemistry structure, and computer sciences. Suppose the set W = {s1,s2,...,sk}⊂ V (G), the vertex representations of x V (G) is rm(x|W) = {d(x,s1),d(x,s2),...,d(x,sk)}, where d(x,si) is the length of the shortest path of the vertex x and the vertex in W together with their multiplicity. The set W is called a local m-resolving set of graphs G if rm(v|W)≠rm(u|W) for uv E(G). The local m-resolving set having minimum cardinality is called the local multiset basis and its cardinality is called the local multiset dimension of G, denoted by mdl(G). In our paper, we determine the establish bounds of local multiset dimension of graph resulting corona product of tree graphs.

KW - Local m -resolving set

KW - corona product

KW - local multiset dimension

KW - tree graphs

UR - http://www.scopus.com/inward/record.url?scp=85179826209&partnerID=8YFLogxK

U2 - 10.1142/S1793830923500921

DO - 10.1142/S1793830923500921

M3 - Article

AN - SCOPUS:85179826209

SN - 1793-8309

JO - Discrete Mathematics, Algorithms and Applications

JF - Discrete Mathematics, Algorithms and Applications

M1 - 2350092

ER -