Graphs with maximal irregularity
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 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.
Graphs with maximal irregularity
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WebSep 15, 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. WebFeb 19, 1999 · The graphs with maximal total irregularity are determined. It is also shown that among all trees of same order the star graph has the maximal total irregularity. View.
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 … 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 …
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 … WebRecently, this graph invariant gained interest in the chemical graph theory, where (PDF) Graphs with maximal irregularity Darko Dimitrov - Academia.edu Academia.edu no …
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, …
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 ... raymond bilodeauWebAs 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 … raymond bigot peintreWeb3. 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 … raymond biggs west shore bankWeb3. 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 … raymond bigelow judgeWebMar 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. raymond bilottWebMar 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 … raymond billeaudWebDec 1, 2024 · The extremal irregularity of connected graphs with given number of pendant vertices. The irregularity of a graph G = (V, E) is defined as the sum of imbalances ∣du … simplicity crib manual