Graphs with maximal irregularity

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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. WebRecently, this graph invariant gained interest in the chemical graph theory, where (PDF) Graphs with maximal irregularity Darko Dimitrov - Academia.edu Academia.edu no …

The extremal irregularity of connected graphs with given number …

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 … 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 … radio đakovo live stream

Graphs with maximal irregularity ScienceGate

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, … 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 … 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 ... dq blackboard\\u0027s

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Graph irregularity and its measures - ScienceDirect

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 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 … dq banjo\u0027sWebIn 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 … dq blackboard\u0027s

"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. " - Graphs with maximal irregularity

Graphs with maximal irregularity

Irregularity Measures of Subdivision Vertex-Edge Join of Graphs - Hindawi

WebAlizadeh 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 … 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 …

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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. 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.

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 … 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 ...

WebDec 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 … 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.

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 …

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 … radio đakovo umrliWebSep 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 … dq bivalve\\u0027sWebJan 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. radio dakovo uzivoWebMar 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 … radio dak uzivoWebWe 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 … dq Bokm\\u0027WebDec 11, 2024 · General graphs with maximal σ irregularity. In order to characterize graphs with maximal σ irregularity, we first determine the minimum number of … radio đakovo uživoWebSep 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. radio đakovo facebook