The harmonic index for graph

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August undefined, 2024

WebThis idea has resurfaced several time in the literature, often without the normalization factor : for undirected graphs under the name valued centrality by Dekker (2005) [23] and under the name harmonic centrality by Rochat (2009); [24] if was axiomatized by Garg (2009) [25] and proposed once again later by Opsahl (2010). [26] WebThe harmonic index of a graph G G is defined as the sum of weights 2 d(v)+d(v) 2 d ( v i) + d ( v j) of all edges vivj v i v j of G G, where d(vi) d ( v i) denotes the degree of the vertex vi v i in G G. In this paper, we study how the harmonic index behaves when the graph is …

Harmonic Matrix and Harmonic Energy - CORE

WebA complete graph is a graph in which each pair of graph vertices is connected by an edge. The complete graph with n graph vertices is denoted K. n and has n(n 1)/2 undirected edges. The Harmonic Index [7], [4] of a graph G is defined by 𝐻(𝐺) = 2 𝑑𝑢+ 𝑑𝑣 Where (u,v) is an element of E(G). Motivated by the definition of Zagreb ... Web15 Nov 2024 · Proposition 3.4. The second hyper-Zagreb coindex of aspirin. From the graph structure of aspirin (Figure 2), it is easy to obtain the dataset in Tables 2 and 3.. Also, by Table 4 and definition of the second hyper-Zagreb index, we have. Using Proposition 3.2, we have. Nicotine (C 10 H 14 N 2) is an alkaloid that is widely used as an anxiolytic.Nicotine … roblox shirt ideas template

Relations between some topological indices and the line graph

Web7 Jan 2024 · The graph theory is a significant part of applied mathematics for modeling real life problems. The chemical graph theory, a fascinating branch of graph theory, provides many information on chemical compounds using an important tool called the topological index [4, 43].Theoretical molecular descriptors alias topological indices are graph … Web12 hours ago · These 9 analysts have an average price target of $19.56 versus the current price of Harmonic at $15.81, implying upside. Below is a summary of how these 9 analysts rated Harmonic over the past 3 ... WebHarmonics are voltages or currents that operate at a frequency that is an integer (whole-number) multiple of the fundamental frequency. So given a 50Hz fundamental waveform, this means a 2nd harmonic frequency would be 100Hz (2 x 50Hz), a 3rd harmonic would be 150Hz (3 x 50Hz), a 5th at 250Hz, a 7th at 350Hz and so on. roblox shirt ids for 0 robux

Harmonic index of a line graph - ScienceDirect

(PDF) The Harmonic Index for Bicyclic Graphs - ResearchGate

Web15 Nov 2024 · Abstract. The harmonic index of a connected graph G, denoted by H(G), is defined as H(G) = ∑ uv∈E(G) 2 du+dv where dv is the degree of a vertex v in G. Web30 Jan 2024 · The harmonic index H ( G) of G is defined as H ( G) = ∑ u v ∈ E ( G) 2 d u + d v. At the very beginning of development of chemical graph theory, Gutman and Trinajstić considered also an invariant defined as the sum of cubes of vertex degrees [15]. roblox shirt ids for 200 robuxWebThe unicyclic graphs with maximum and mini- mum harmonic index among all unicyclic graphs of order n were deter- mined by Zhong [9]. In this section, using Theorems 3.1, 3.4 and 3.5, we provide a simpler method for determining the unicyclic graphs with maximum and minimum harmonic index among all unicyclic graphs of order n, respectively. roblox shirt ids list 10 robux

"Web11 Dec 2015 · The harmonic index of a graph G is defined as the sum of weights $\frac{2}{d(u)+d(v)}$ over all edges uv of G, where d(u) and d(v) are the degrees of the vertices u and v in G, respectively. " - The harmonic index for graph

The harmonic index for graph

Full article: Eccentric harmonic index of a graph - Taylor & Francis

Web15 Apr 2012 · The harmonic index of a graph is defined as the sum of weights of all edges of , where denotes the degree of a vertex in . In this note we generalize results of [L. Zhong, The harmonic index on graphs, Appl. Math. Lett. 25 (2012), 561--566] and establish some upper and lower bounds on the harmonic index of . Comments: Web30 Sep 2024 · The harmonic index of a graph is defined as the sum of the weights of all edges of , where is the degree of the vertex in . The -chromatic number of , denoted by , is the minimum number such that is - -colorable. In this paper, we show that , and the equality holds if and only if is a complete graph possibly with some additional isolated vertices.

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Web25 Sep 2024 · As examples, Favaron, Mahéo and Saclé considered the relationships between the harmonic index and the eigenvalues of graphs, and Zhong and Xu [51, 58, 59] determined the minimum and maximum values of the harmonic index for connected graphs, trees, unicyclic graphs, and bicyclic graphs, and characterized the corresponding extremal … WebThe maximum value of the harmonic centralization is deﬁned through the study of the index on a star graph. The index of the node in the center is 1 and 1 1 1 n of the leaves is n−1 ( 1 + (n − 2) 2 ) = 2(n−1) . Therefore centralization index of harmonic centrality is X ∗ 2(n − 1) cH − cH (xi) (8) C = i H n ∗ with c = max cH (xj) and n = V . H j

Web16 Feb 2024 · The harmonic index of a graph () is defined as the sum of the weights for all edges of , where is the degree of a vertex in . In this paper, we show that and , where is a quasi-tree graph of order and diameter . Indeed, we show that both lower bounds are tight and identify all quasi-tree graphs reaching these two lower bounds. 1. Introduction Web1 Nov 2016 · In this paper we have defined the harmonic status index of a graph G as and obtained the bounds for HS ( G ). Further the harmonic status index of some graphs is obtained. Regression...

Web1 Mar 2012 · The harmonic index of a graph G is defined as the sum of the weights 2 d (u) + d (v) of all edges u v of G, where d (u) denotes the degree of a vertex u in G. In this work, we present the minimum and maximum values of the harmonic index for simple connected graphs and trees, and characterize the corresponding extremal graphs. Web1 Apr 2024 · The harmonic index of a conected graph G is deﬁned as H(G) = ∑ uv∈E(G) 2 d(u)+d-(v), where E(G) is the edge set of G, d(u) and d(v) are the degrees of vertices u and v, respectively. The spectral radius of a square matrix M is the maximum among the absolute values of the eigenvalues of M.

Web15 Apr 2012 · The harmonic index of a graph G is defined as the sum of weights $\frac{2}{d(u)+d(v)}$ over all edges uv of G, where d(u) and d(v) are the degrees of the vertices u and v in G, respectively.

WebThe harmonic index of a graph Gis deﬁned as the sum of the weights 2 d(u)+d(v) of all edges uv of , where d(u) denotes the degree of a vertex u in G. In this work, we present the minimum, second-minimum, maximum and second-maximum harmonic indices for unicyclic graphs with given girth, and characterize roblox shirt ids for boys 2022WebA subdivision graph of a given graph G is derived from G by inserting a new vertex into the middle point of each edge of G. 1,2 The line graph of a graph G is the graph whose vertices are in a one-to-one correspondence with the edges of G and two vertices are connected if and only if their corresponding edges are share a common vertex in G. 3,4 The degree of a … roblox shirt ids that are 20 robuxWebThe harmonic index of a connected graph G ‎, ‎denoted by H (G) ‎, ‎is‎ ‎defined as H (G)=∑ uv∈E (G) 2d u +d v ‎ ‎where d v is the degree of a vertex v in G‎. In this paper‎, ‎expressions for the Harary indices of the‎ ‎join‎, ‎corona product‎, ‎Cartesian product‎, ‎composition and … roblox shirt ids starving artistsWeb5 Dec 2024 · The concepts of geometric–arithmetic and harmonic indices were introduced in the area of chemical graph theory recently. They have proven to correlate well with physical and chemical properties of some molecules. The aim of this paper is to obtain new inequalities involving the first Zagreb, the harmonic, and the geometric–arithmetic GA_1 ... roblox shirt ids that are 10 robux roblox shirt images pngWebhow the harmonic index behaves when the graph is perturbed by sep-arating, grafting or deleting an edge. These results are used to provide a simpler method of determining the unicyclic graphs with maximum and minimum harmonic index among all unicyclic graphs of order n, respectively. 2. Lower bounds for harmonic index. In this section, we estab- roblox shirt keywordsWeb15 Apr 2012 · On the Harmonic Index of Unicyclic Conjugated Molecules. Yan Zhu, Renying Chang. Mathematics. 2015. The harmonic index H(G) of a graph G is defined as the sum of weights 2 d(u) + d(v) of all edges uv of G, where d(u) denotes the degree of a vertex u in G. In this paper, we first present a sharp…. roblox shirt in template