A molecular (chemical) graph is a simple connected graph, where the vertices represent the compou... more A molecular (chemical) graph is a simple connected graph, where the vertices represent the compound's atoms and the edges represent bonds between the atoms, and the degree (valence) of every vertex (atom) is not more than four. In this paper, we determine the edge metric basis and edge metric dimension (EMD) of the complex molecular graph of a one-heptagonal carbon nanocone (HCN 7 (q)). We prove that only three non-adjacent vertices are the minimum requirement for the identification of all the edges in HCN 7 (q), uniquely. INDEX TERMS Connected graph, edge metric basis, edge metric dimension, independent set, oneheptagonal carbon nanocone, resolving set.
Let Γ = (V,E) be a simple connected graph. d(α, ) = min{d(α,w), d(α, d} computes the distance bet... more Let Γ = (V,E) be a simple connected graph. d(α, ) = min{d(α,w), d(α, d} computes the distance between a vertex α ∈ V (Γ) and an edge = wd ∈ E(Γ). A single vertex α is said to recognize (resolve) two different edges 1 and 2 from E(Γ) if d(α, 2) 6= d(α, 1}. A subset of distinct ordered vertices UE ⊆ V (Γ) is said to be an edge metric generator for Γ if every pair of distinct edges from Γ are recognized by some element of UE . An edge metric generator with a minimum number of elements in it, is called an edge metric basis for Γ. Then, the cardinality of this edge metric basis of Γ, is called the edge metric dimension of Γ, denoted by edim(Γ). The concept of studying chemical structures using graph theory terminologies is both appealing and practical. It enables chemical researchers to more precisely and easily examine various chemical topologies and networks. In this article, we investigate a fascinating cluster of organic chemistry as a result of this motivation. We consider a zigzag ...
A molecular (chemical) graph is a simple connected graph, where the vertices represent the compou... more A molecular (chemical) graph is a simple connected graph, where the vertices represent the compound's atoms and the edges represent bonds between the atoms, and the degree (valence) of every vertex (atom) is not more than four. In this paper, we determine the edge metric basis and edge metric dimension (EMD) of the complex molecular graph of a one-heptagonal carbon nanocone (HCN 7 (q)). We prove that only three non-adjacent vertices are the minimum requirement for the identification of all the edges in HCN 7 (q), uniquely. INDEX TERMS Connected graph, edge metric basis, edge metric dimension, independent set, oneheptagonal carbon nanocone, resolving set.
Let Γ = (V,E) be a simple connected graph. d(α, ) = min{d(α,w), d(α, d} computes the distance bet... more Let Γ = (V,E) be a simple connected graph. d(α, ) = min{d(α,w), d(α, d} computes the distance between a vertex α ∈ V (Γ) and an edge = wd ∈ E(Γ). A single vertex α is said to recognize (resolve) two different edges 1 and 2 from E(Γ) if d(α, 2) 6= d(α, 1}. A subset of distinct ordered vertices UE ⊆ V (Γ) is said to be an edge metric generator for Γ if every pair of distinct edges from Γ are recognized by some element of UE . An edge metric generator with a minimum number of elements in it, is called an edge metric basis for Γ. Then, the cardinality of this edge metric basis of Γ, is called the edge metric dimension of Γ, denoted by edim(Γ). The concept of studying chemical structures using graph theory terminologies is both appealing and practical. It enables chemical researchers to more precisely and easily examine various chemical topologies and networks. In this article, we investigate a fascinating cluster of organic chemistry as a result of this motivation. We consider a zigzag ...
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Papers by Karnika Sharma