Distance-based topological indices and forwarding indices of circulant graphs

• Main Author: Antalan, John Rafael M.
• Format: text
• Language: English
• Published: Animo Repository 2021
• Subjects: Indexes; Topological graph theory; Mathematics
• Online Access: https://animorepository.dlsu.edu.ph/etdd_math/2; https://animorepository.dlsu.edu.ph/cgi/viewcontent.cgi?article=1001&context=etdd_math
• Institution: De La Salle University

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.