Graphs with maximal irregularity
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]. 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, …
Graphs with maximal irregularity
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WebJan 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. 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 ...
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’, …
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. 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 …
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 …
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 … descargar sin city 2WebMar 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. chrysler capital 10 day payoffWebJul 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 … chrysler capital 10 day payoff phone numberWebWe 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 … chrysler capital 3000 kellway driveWebHere, 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 chrysler capital 1800WebWe 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 chrysler.ca pacificaWebMar 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. chrysler can am warranty