WebHere, we characterise the nonregular graphs with minimal total irregularity and thereby resolve the recent conjecture by Zhu et al. [‘The minimal total irregularity of graphs’, Preprint, 2014, arXiv:1404.0931v1] about the lower bound on the minimal total WebIn order to characterize graphs with maximal irregularity, we rst determine the minimum number of universal vertices that such graphs must have. Lemma 2.1. Let Gbe a graph with maximal irregularity among all graphs of order n. Then, Ghas at least n 3 universal vertices. Proof. Assume that Gis a graph with maximal irregularity whose set U of ...
Irregularity Measure of Graphs
WebFeb 28, 2024 · Graph-theoretic irregularity indices have diverse applications in computer science. This paper extends their practical applicability in reticular chemistry. First, we put forward a method of computing various irregularity indices of graphs by means of their main eigenvalues. This presents applications of spectral graph theory in chemistry. We … WebSep 15, 2024 · It seems that the oldest numerical measure of graph irregularity was proposed by Collatz and Sinogowitz [20] who defined it as C S ( G) = λ 1 − 2 m n where λ1 is the largest eigenvalue of the adjacency matrix, usually referred to as the spectral radius of the underlying graph [21], [38]. simpson strong tie sdws timber screw
(PDF) Graphs with Maximal Irregularity - ResearchGate
WebDec 11, 2024 · General graphs with maximal σ irregularity. In order to characterize graphs with maximal σ irregularity, we first determine the minimum number of … WebJul 28, 2024 · An inclusive distance vertex irregular labeling of a graph G is an assignment of positive integers \(\{1, 2, \ldots , k\}\) to the vertices of G such that for every vertex the sum of numbers assigned to its closed neighborhood is different. The minimum number k for which exists an inclusive distance vertex irregular labeling of G is denoted by … WebApr 20, 2024 · The irregularity of a graph G = (V, E) is defined as the sum of imbalances ∣du − dv∣ over all edges uv ∈ E, where du denotes the degree of the vertex u in G. This graph invariant, introduced by Albertson in 1997, is a measure of the defect of regularity of a graph. In this paper, we completely determine the extremal values of the irregularity of … simpson strong tie self drilling screws