Distance-based topological indices and forwarding indices of circulant graphs

Clicks: 3
ID: 286885
2021
Free PDF
Article Quality & Performance Metrics
Overall Quality
Not rated
Combines reader engagement with the AI quality analysis. This article has not been analysed, so there is no overall score — reader engagement is measured and shown alongside.
AI Quality Assessment
Not analyzed
Readership in this journal
Steady

Ranked #3,116 of 3,757 articles by views in Malay Journal

Most read Least read

Bar heights use a square-root scale. Only the 120 most-read articles are drawn; the journal has 3,757 in total.

Mint this article as an NFT
Not yet minted

Create a permanent, verifiable on-chain record of this article on the Scimatic Network. The NFT is held in your Journament account, and you can withdraw it to your own wallet at any time.

5 SUSD one-off · no wallet required
Sign in to mint
Abstract
Let $\cal{G}$ be a family of graphs. A \textit{topological index} is a function $Top:\cal{G}\to \mathbb{R}$ such that if $\Gamma_1,\Gamma_2\in \cal{G}$, and $\Gamma_1\cong \Gamma_2$ then $Top(\Gamma_1)=Top(\Gamma_2)$. If $v_i$ and $v_j$ are vertices in a graph, the distance between them refers to the length of a shortest path that connects $v_i$ and $v_j$. A topological index is said to be distance-based if its computation involves distance between vertices of a graph. On the other hand, given a graph of order $n$, a collection of $n(n-1)$ simple paths connecting every ordered pair of vertices of the graph is called a \textit {routing} of the graph. The \textit{vertex-forwarding index} of a graph with respect to a given routing refers to the maximum number of paths in the routing that passes through any vertex of the graph. The \textit{vertex-forwarding index} of a graph refers to the minimum vertex-forwarding index over all possible routing of the graph. The \textit{edge-forwarding index} of a graph is defined similarly. Topological indices have vast applications in the field of Chemistry, while forwarding indices are used in network analysis. In this dissertation, we compute for some well known distance-based topological indices as well as for the exact value of the vertex-forwarding index of certain families of circulant graph class. We also find some bounds for the edge-forwarding index of the circulant graphs under consideration. Finally, we look at how the graph operation ``shadow of a graph" affects the values of the distance-based topological indices of circulant graphs.
Reference Key
persistent_1760659953_68f189f1ad871 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Antalan, John Rafael M.
Journal Malay Journal
Year 2021
DOI
DOI not found
URL
https://animorepository.dlsu.edu.ph/etdd_math/2
Keywords Keywords not found

Citations

No citations found. To add a citation, contact the admin at info@scimatic.org

Comments

No comments yet. Be the first to comment on this article.