Graphs with maximal irregularity

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August undefined, 2024

WebA graph is thus locally irregular if for each vertex v of G the neighbors of v have distinct degrees, and these graphs are thus termed highly irregular graphs. Properties of … WebMar 20, 2024 · Abstract. A simple graph is said to be regular if its vertices have the same number of neighbors. Otherwise, is nonregular. So far, various formulas, such as the Albertson index, total Albertson index, and degree deviation, have been introduced to quantify the irregularity of a graph. In this paper, we present sharp lower bounds for …

Variable neighborhood search for extremal graphs. 16

WebSep 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 … WebDec 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 … cylinder inspection form

Graph irregularity and its measures - ScienceDirect

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 ... Web3. Lower Bounds on Graphs with Maximal Irregularity. The authors consider graphs with maximal irregularity and prescribed minimal or/and maximal degrees. First, the authors show a lower bound for graphs with … 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 cylinder inspection liability form

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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 … 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 cylinder inspection courseWebDec 11, 2024 · General graphs with maximal σ irregularity. In order to characterize graphs with maximal σ irregularity, we first determine the minimum number of … cylinder inspection report

"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 ... " - Graphs with maximal irregularity

Graphs with maximal irregularity

The extremal irregularity of connected graphs with given number …

WebNov 25, 2024 · Abstract. We prove a sharp upper bound on the number of shortest cycles contained inside any connected graph in terms of its number of vertices, girth, and maximal degree. Equality holds only for Moore graphs, which gives a new characterization of these graphs. In the case of regular graphs, our result improves an inequality of Teo and Koh. WebMar 15, 2024 · Abdo et al. [2] determined all graphs with maximal total irregularity and proved that among all trees of the same order the star has the maximum total irregularity. You et al. [7], investigated the total irregularity of bicyclic graphs and characterized the graph with the maximal total irregularity among all bicyclic graphs on n vertices.

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WebAs a standard notation, assume that G = G(V,E) is a finite, simple and undirected graph with p vertices and q edges. A labeling of a graph is any mapping that sends some set of graph elements to a set of numbers (usually positive integers). If the domain is the vertex-set or the edge-set, the labelings are called respectively vertex-labelings or edge-labelings. If the … WebDec 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, …

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 … 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 …

WebIn order to characterize graphs with maximal irregularity, we ﬁrst determine the minimum number of universal vertices that such graphs must have. Lemma 2.1. Let G be a graph … WebMar 1, 2024 · Recently, Gutman introduced the class of stepwise irregular graphs and studied their properties. A graph is stepwise irregular if the difference between the degrees of any two adjacent vertices is exactly one. In this paper, we get some upper bounds on the maximum degree and sharp upper bounds on the size of stepwise irregular graphs.

WebJul 25, 2024 · The irregularity of a graph is the sum of the absolute values of the differences of degrees of pairs of adjacent vertices. In this paper, we obtain an upper bound on the irregularity of graphs in terms of the order, the size and the number of pendant …

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]. cylinder inspection trainingWebMar 15, 2024 · Abdo et al. [2] determined all graphs with maximal total irregularity and proved that among all trees of the same order the star has the maximum total … cylinder inspection requirementsWebMar 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. cylinder in spherical coordinatesWebJan 18, 2024 · The study of graphs and networks accomplished by topological measures plays an applicable task to obtain their hidden topologies. This procedure has been greatly used in cheminformatics, bioinformatics, and biomedicine, where estimations based on graph invariants have been made available for effectively communicating with the … cylinder in tagalogWebRecently, this graph invariant gained interest in the chemical graph theory, where (PDF) Graphs with maximal irregularity Darko Dimitrov - Academia.edu Academia.edu no … cylinder insulationWebWe 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 … cylinder insulation jacketWebIrregularity 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 … cylinder intersection