Graphs with maximal irregularity
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. 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 …
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. 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.
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 ... 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 …
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 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 … dan rayfield speaker of the houseWebRecently, this graph invariant gained interest in the chemical graph theory, where (PDF) Graphs with maximal irregularity Darko Dimitrov - Academia.edu Academia.edu no … dan raymond attorneyWebIrregularity 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 … birthday party entertainment for toddlersWebSep 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]. danr contractor certification formWebDec 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 … dan raynor american bridgeWebAs 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 … dan raz city of hopeWebWe 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 birthday party entertainment frisco tx