Wiener Index of Nanotubes, Toroidal Fullerenes and Nanostars

Ашрафи, Али Реза

doi:10.1007/978-94-007-0221-9_2

Cited by 5 publications

(5 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For instance, let H be the molecular graph of the polyhex nanotorus whose 2-dimensional lattice is depicted in Figure 3. It is cubic, 184-transmission regular, which is vertex-transitive [32]. Therefore WH(H) = 184 3 A(H).…”

Section: Example 2 Let G Be a Connected Graph Such Thatmentioning

confidence: 99%

Wiener–Hosoya Matrix of Connected Graphs

et al. 2021

View full text Add to dashboard Cite

Let G be a connected (molecular) graph with the vertex set V(G)={v1,⋯,vn}, and let di and σi denote, respectively, the vertex degree and the transmission of vi, for 1≤i≤n. In this paper, we aim to provide a new matrix description of the celebrated Wiener index. In fact, we introduce the Wiener–Hosoya matrix of G, which is defined as the n×n matrix whose (i,j)-entry is equal to σi2di+σj2dj if vi and vj are adjacent and 0 otherwise. Some properties, including upper and lower bounds for the eigenvalues of the Wiener–Hosoya matrix are obtained and the extremal cases are described. Further, we introduce the energy of this matrix.

show abstract

Section: Example 2 Let G Be a Connected Graph Such Thatmentioning

confidence: 99%

Wiener–Hosoya Matrix of Connected Graphs

et al. 2021

View full text Add to dashboard Cite

show abstract

“…It is regular of degree 3 and has pq vertices and 3 pq 2 edges. The following lemma was proved in [39,43].…”

Section: Lemma 38 ([42]mentioning

confidence: 99%

Status connectivity indices and co-indices of graphs and its computation to some distance-balanced graphs

Ramane

Yalnaik

Sharafdini

2020

AKCE International Journal of Graphs and Combinatorics

View full text Add to dashboard Cite

show abstract

“…On the other hand, the map θ defined by θ(u ij ) = θ(u (p+1−i)j ) is a graph omorphism of T and so if "i is odd and r is even" or "i is even and r is odd" then in u ij and u rs will be in the same orbit of Aut(G), proving the lemma. The following Lemma was proved in [1] and [29].…”

Section: Mmamentioning

confidence: 99%

Vertex weighted Laplacian graph energy and other topological indices

Sharafdini¹,

Panahbar²

2016

Preprint

View full text Add to dashboard Cite

Let G be a graph with a vertex weight ω and the vertices v 1 , . . . , v n . The Laplacian matrix of G with respect to ω is defined asThen the Laplacian energy of G with respect to ω defined asIn this paper we consider several natural vertex weights of G and obtain some inequalities between the ordinary and Laplacian energies of G with corresponding vertex weights. Finally, we apply our results to the molecular graph of toroidal fullerenes (or achiral polyhex nanotorus).

show abstract

Wiener Index of Nanotubes, Toroidal Fullerenes and Nanostars

Cited by 5 publications

References 21 publications

Wiener–Hosoya Matrix of Connected Graphs

Wiener–Hosoya Matrix of Connected Graphs

Status connectivity indices and co-indices of graphs and its computation to some distance-balanced graphs

Vertex weighted Laplacian graph energy and other topological indices

Contact Info

Product

Resources

About