Average Detour D-Distance in Graphs

Abstract

This paper considers Linear two-parameter eigenvalue problems in terms of matrix operators. Generally, for spectral analysis two-parameter problem is reduced into a system of generalized eigenvalue problems using a special pair of determinant operator matrices on tensor product space. In this work, some inequalities on numerical range and numerical radius of this special pair of operator matrices arising from two-parameter problem will be derived.

Computation of Detour D-Index and Average Detour D-Distance of Specific Graphs

“…In graph theory, the average distance is a crucial parameter, serving as a key parameter in analytic networks. This metric's significance lies in the fact that the time required for performance is directly related to the distance between two points within the network [11] .…”

“…Definition 1.3: [11] Let 𝛬 be a connected graph, of order 𝜚, then the average DDD of 𝛬 indicated by 𝜇 𝐷 𝐷 (𝛬) and defined as…”

Average circular D-distance and circular D-Wiener index of K-regular graphs

“…In addition to the geodesic distance, ( ) , d r s , we have detour distance (introduced by Chartrand et al in [3], average distance and dominating number (introduced by Dankelmann in [4,5] ), mean distance in graphs (introduced by Doyale in [6] ), superior distance (introduced by Kathiresan and Marimuthu in [7] ), signal distance (introduced by Kathiresan and Marimuthu in [8] ), average D -distance (introduced by Reddy babu, Varma in [11] ), average detour D -distance (introduced by Venkateswara Rao, Varma in [12] ).…”