Graphs with maximal irregularity
Webvertex of degree n - 1. If irr(e ) = n - 2 would hold for all edges of a graph, then this graph would have maximal irregularity. In the case of trees, this condition is obeyed by the star (and only by it). Thus we arrive at the following simple result: Lemma 1.2. Among trees of ordern, the star Sn is the unique tree with greatest irregularity ... 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 …
Graphs with maximal irregularity
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WebWe also present lower bounds on the maximal irregularity of graphs with fixed minimal and/or maximal vertex degrees, and consider an approximate computation of the irregularity of a graph. Download Full-text. Related Documents; Cited By; References; Molecular Descriptors of Nanotube, Oxide, Silicate, and Triangulene Networks WebJan 30, 2024 · The maximum degree of a graph G is denoted by Δ (G). Lemma 2. Let k and n be fixed integers satisfying 0 ≤ k ≤ n − 2. If G is a graph possessing the greatest sigma index over the family of all connected k-cyclic graphs of order n, then Δ (G) = n − 1. Proof. Contrarily, assume that v ∈ V (G) such that d v = Δ (G) ≤ n − 2.
WebRecently, this graph invariant gained interest in the chemical graph theory, where (PDF) Graphs with maximal irregularity Darko Dimitrov - Academia.edu Academia.edu no …
WebIrregularity indices are usually used for quantitative characterization of the topological structures of non-regular graphs. In numerous problems and applications, especially in the fields of chemistry and material engineering, it is useful to be aware of the irregularity of a molecular structure. Furthermore, the evaluation of the irregularity of graphs is valuable … WebMar 16, 2024 · The mentioned authors determined all graphs with maximal total irregularity. They also shown that the star graph has the maximum total irregularity in the class of all n -vertex trees. Abdo and Dimitrov [ 1 ], obtained upper bounds for the total irregularity of some graph operations in terms of the total irregularity of their factors.
WebOct 30, 2024 · Modular Irregularity Strength of Triangular Book Graph. M. I. Tilukay. Mathematics. ArXiv. 2024. This paper deals with the modular irregularity strength of a graph of nn vertices, a new graph invariant, modified from the irregularity strength, by changing the condition of the vertex-weight set…. 1.
WebDec 1, 2014 · The maximum irregularity of bipartite graphs [8], graphs of bounded clique number [12], and graphs with a given number of vertices of degree 1 [4,9] was also … inzichtkaarten a beautiful storyWebDec 16, 2008 · The most irregular connected graph on n (n ⩾ 10) vertices is a pineapple PA (n, q) in which the clique size q is equal to ⌈ n 2 ⌉ + 1. Extremal graphs have been obtained by AGX and recognized to be complete split graphs for n = 10, 11, …, 17. For smaller values of n the maximal graph is again a pineapple (reduced to a star for n = 5, … on screen scriptWebHere, 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’, … inzident graphentheorieWebDec 28, 2024 · Abstract. A modular irregular graph is a graph that admits a modular irregular labeling. A modular irregular labeling of a graph of order is a mapping of the set of edges of the graph to such that the weights of all vertices are different. The vertex weight is the sum of its incident edge labels, and all vertex weights are calculated with the sum … on screen scoreboardWebAlizadeh et al. (2024) studied the irregularity of π-permutation graphs, Fibonacci cubes, and trees. Hansen and Mélot (2005) characterized the graphs of order n and size m that … onscreen serviceWebHere, 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 on screen screenshot on hp laptopWebSep 1, 2024 · Here, we characterize general graphs with maximal σ irregularity. We also present lower bounds on the maximal σ irregularity of graphs with fixed minimal and/or … on screen sharing