Jul 2026· Scientific Annals of Computer Science· Vol 36, pp. 107· 0 citations· 29 references
TL;DR
An explicit spectral construction is developed enabling the numerical validation algorithm to evaluate the time complexity in various structural configurations of (2n+1)-graphs, highlighting the substantial algorithmic demands for several graphs.
Abstract
This study investigates the path energy bounds of hub-centric graph families of order (2n+1), denoted by ℋ2n+1. The path energy is defined as the absolute sum of the eigenvalues of the path adjacency matrix Ap(ℋ2n+1), where each entry pij measures the maximum number of internally vertex- disjoint paths. Through an in-depth examination of the characteristic values of this matrix Ap(ℋ2n+1), we derive path energy bounds specific to these four (2n+1)-vertex graph, namely closed helm, double star, friendship, and double wheel graphs. We further developed an explicit spectral construction enabling the numerical validation algorithm to evaluate the time complexity in various structural configurations of (2n+1)-graphs. Also executed extensive trials to capture their average, maximum, and minimum computational performances. This analysis offers a detailed comparative study of the structural attributes that lead to computational complexity, highlighting the substantial algorithmic demands for several graphs.
This study explores the spectral characteristics and energy distributions associated with selected graph operations derived from the first Zagreb, second Zagreb, and sum-connectivity matrices to contribute to understanding how algebraic operations induce spectral energy shifts analogous to perturbations in physical or...
S. Sripriya, A. Anuradha· Baghdad Science Journal· 0 citations
This paper presents a comparative analysis of two variants of a classical algorithm for finding the shortest path in a connected graph. The first variant uses an adjacency matrix (AM) to verify the existence of an edge (arc) between two vertices, while the second variant performs the same verification using an adjacenc...
V. Kralev, Radoslava Kraleva, Aleksandra Popova· International Journal of Int...· 0 citations
The concept of graph energy, defined as the sum of the absolute eigenvalues of a graph's adjacency matrix, has been widely studied for its applications in chemistry and network theory. In this paper, we extend this notion to k-uniform hypergraphs by introducing the domination energy, a spectral invariant derived from a...
Abdulkafi Sanad, S. Mahde, Abdulqawe Kaed· International Journal of Wav...· 0 citations
The ‘divide and conquer’ paradigm proves to be one of the most frequently used techniques for dealing with the complexities of graph-related problems. Therefore, it is of great importance to measure the tendency of a vertex to be critical and its susceptibility in a graph. The criticality of a vertex is often analysed...
Saifur Rahman, Raju Doley· Acta Universitatis Sapientia...· 0 citations
Investigating the energy complexity of several well-studied (local) problems in distributed graph algorithms—namely, matching and vertex cover approximations, spanners, low-outdegree orientations, and set cover, presents randomized distributed algorithms that achieve nearly exponentially smaller energy complexity.
Mohsen Ghaffari, Zi Song Yeoh· ACM Symposium on Parallelism...· 1 citation
Gupta and Iosevich introduced the edge complexity of a graph as the minimum Fourier ratio of its adjacency matrix over all vertex labelings and bounded it below by graph energy divided by the square root of twice the number of edges. We characterize equality for a fixed labeling: the Fourier transform of the adjacency...
Vishal Gupta, A. Iosevich, J. Iosevich et al.· 0 citations
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