Group analysis and numerical approximation of proliferating and maturing cellular populations model

Noori Eskandari, Mohammad Hadi; Hejazi, S. Reza; Erfanian Oraei Dehrokhi, Hamid

doi:10.22060/ajmc.2025.23231.1243

Group analysis and numerical approximation of proliferating and maturing cellular populations model

Document Type : Original Article

Authors

Mohammad Hadi Noori Eskandari

S. Reza Hejazi

Hamid Erfanian Oraei Dehrokhi

Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran

10.22060/ajmc.2025.23231.1243

Abstract

Locating or resolving sets are introduced as a graph-theoretic model of robot navigation and has different applications in diverse areas like network discovery, computer science and chemistry. These applications leads to some graph parameters, like the metric dimension and the adjacency dimension. A subset $S$ of the vertices of a graph $G$ is an adjacency resolving set for $G$ if for each pair of distinct vertices $x, y \in V(G)\setminus S$, there exists $s \in S$ which is adjacent to exactly one of these two vertices. An adjacency resolving set with the minimum cardinality is called an adjacency basis and its cardinality is the adjacency dimension of $G$. Since the problem of computing the adjacency dimension of a graph is NP-hard, finding the adjacency dimension of special classes of graphs or obtaining good bounds on this invariant is valuable. In this paper we determine the adjacency dimension of some famous star related trees.

Keywords

Lie symmetry

Jacobi-pesudo-spectral method

Delay differential equations

Subjects