The generalized distance matrix of a connected graph G, denoted by Dα(G), is defined as (formula presented). Here, D(G) is the distance matrix and T r(G) represents the vertex transmissions. Let (formula presented) be the eigenvalues of Dα(G) and let W (G) be the n∑ Wiener index. The generalized distance energy of G can be defined as (formula presented) In this paper, we develop some new theory regarding the generalized distance energy EDα (G) for a connected graph G. We obtain some sharp upper and lower bounds for EDα (G) connecting a wide range of parameters in graph theory including the maximum degree ∆, the Wiener index W (G), the diameter d, the transmission degrees, and the generalized distance spectral spread DαS(G). We characterized the special graph classes that attain the bounds. i=1.
|Number of pages||14|
|Journal||Journal of Algebra Combinatorics Discrete Structures and Applications|
|Publication status||Published - 10 May 2023|