The harmonic index for graph
Web15 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…. 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:
The harmonic index for graph
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Web1 Nov 2013 · Let G be a simple graph with the chromatic number χ ( G) and the harmonic index H ( G), then χ ( G) ≤ 2 H ( G) with equality if and only if G is a complete graph possibly with some additional isolated vertices. Proof If G is a complete graph possibly with some additional isolated vertices, then χ ( G) = 2 H ( G). WebReturns the Estrada index of a the graph G. Harmonic Centrality# harmonic_centrality (G[, nbunch, distance, ...]) Compute harmonic centrality for nodes. Dispersion# dispersion (G[, u, v, normalized, alpha, b, c]) Calculate dispersion between u and v in G. Reaching#
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]
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 Web19 Mar 2024 · Topological indices which are graph invariants derived from molecular graphs of molecules are used in QSPR researches for modeling physicochemical properties of molecules. Topological indices are important tools for determining the underlying topology of a molecule in view of theoretical chemistry.
Web1 Mar 2013 · 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 have determined...
WebThe eccentric harmonic index of some well-known graphs are computed. The starting is with the definition of H e ( G) which is explained in the following definition. Definition 2.1. Let G be a graph with n vertices and m edges. Then the eccentric harmonic index H e ( G) of G is defined as H e ( G) = ∑ v i v j ∈ E 2 e i + e j. Theorem 2.2. family law lawyer corpus christi texasWebA 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 ... coola carpets furniture longreachWebthe harmonic index H(G). For a graph G, the harmonic index H(G) is defined on the arithmetic mean as H(G) = X uv∈E 2 deg(u)+deg(v). In [3] the authors considered the relation between the harmonic index and the eigenvalues of graphs. Zhong in [10] presented the minimum and maximum values of harmonic index on simple connected graphs and trees, family law lawyer feesWeb25 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 … cool a buck walk in coolerWebThe 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 … cool abstract gifsWeb30 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. family law lawyer garfield countyWeb10 Sep 2014 · The harmonic index H\left ( G\right) of a graph G is defined as the sum of the weights \frac {2} {d_ {u}+ d_ {v}} of all edges uv in G, where d_ {u} denotes the degree of a vertex u in G. In this paper, the harmonic indices of polyomino chains are computed. Also, the extremal polyomino chains with respect to harmonic index are determined. family law lawyer flower mound