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 ... 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 …
Graphs with maximal irregularity
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WebJan 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 … 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 …
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. 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.
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.
WebRecently, this graph invariant gained interest in the chemical graph theory, where (PDF) Graphs with maximal irregularity Darko Dimitrov - Academia.edu Academia.edu no …
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 ironton industrial steel shelvingWebA 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 … port wine subWebDec 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 … port wine strainerWebWe 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 … port wine substitutionWebAs 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 … ironton internet and telephoneWebHere, 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 port wine sugar levelWebIrregularity 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 … port wine substitute in recipe