Abstract
Mathematical modeling, coding or labeling with the help of numeric numbers based on the parameter of distance plays a vital role in the studies of the structural properties of the networks such as accessibility, centrality, clustering, complexity, connectivity, modularity, robustness and vulnerability. In particular, various distance based dimensions of the networks are used to rectify the problems in different strata of computer science and chemistry such as navigation, image processing, pattern recognition, integer programming problem, drug discovery and formation of different chemical compounds. In this note, we consider a family of rotationally symmetric and planar networks called by circular ladders consisting of different faced triangles, quadrangles and pentagons. We compute local fractional metric dimensions of the aforesaid networks and study their boundedness. Moreover, our findings at the closure of this note have been summarized in the form of tables and 3-D plots.
Highlights
A network N is an ordered 2-tuple consisting of two sets, set of nodes called vertices V (N) and links between nodes/vertices called set of edges E(N) such that E(N) ⊆ V (N) × V (N)
We have considered a family of rotationally symmetric and planar networks called by circular ladders consisting of different faced triangle, quadrangle and pentagon
We have computed local fractional metric dimension (LFMD) of rotationally-symmetric and planar networks called by triangular circular ladder (Tn), quadrangular circular ladders (Q1n, Q2n) and pentagonal circular ladders (P1n, P2n, P3n, P5n and P7n)
Summary
A network N is an ordered 2-tuple consisting of two sets, set of nodes called vertices V (N) and links between nodes/vertices called set of edges E(N) such that E(N) ⊆ V (N) × V (N). Liu et al.: LFMDs of Rotationally Symmetric and Planar Networks them constitute the family having constant metric dimension. Aisyah et al (2019) defined the concept of local fractional metric dimension (LFMD) and computed it for the corona product of two networks [29]. We have considered a family of rotationally symmetric and planar networks called by circular ladders consisting of different faced triangle, quadrangle and pentagon. ROBOTICS The necessities of system networking gave rise to the studies of distance based dimensions. These are used to rectify the problem of assigning area to an interpolar in a particular system, see [13], [17]. Apart from that the above mentioned facilities will be facilitated with lesser number of robots
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