Harmonic index of graphs
WebA harmonic is a wave with a frequency that is a positive integer multiple of the fundamental frequency, the frequency of the original periodic signal, such as a sinusoidal wave.The … WebThe harmonic index H(G) of a graph 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 …
Harmonic index of graphs
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WebApr 23, 2024 · The inverse sum indeg index of a connected graph G is defined as the sum of the ratio d G ( u) d G ( v) d G ( u) + d G ( v) for all edges uv in the edge set of G, where d G ( u) denotes the degree of a point u. Recently, Pattabiraman [ 7] has obtained bounds for the inverse sum indeg index of graphs. The upper and lower bounds … WebApr 15, 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. …
WebDec 1, 2015 · 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. In this paper, expressions for the Harary indices of the join, corona product, Cartesian product, composition and symmetric difference of graphs are derived. View via Publisher Save to … WebConic Sections: Parabola and Focus. example. Conic Sections: Ellipse with Foci
WebMar 1, 2024 · The harmonic index of a graph G is defined as, where d(u) denotes the degree of a vertex u in G. Let G(n; k) be the set of simple n-vertex graphs with minimum degree at least k. In this work we ... WebMar 22, 2024 · Fuzzy graph theory was invented by Rosenfeld. It is the extension of the work of L.A. Zadeh on fuzzy sets. Rosenfeld extracted the fuzzy-related concepts using the graph theoretic concepts. Topological indices for crisp theory have already been discussed in the literature but these days, topological index-related fuzzy graphs are much …
We also give inequalities between the eigenvalues and some other … The results, characterizing graphs with maximum χ-values, stated in the … Let Q 1 and Q 2 be two vertex–disjoint connected graphs with at least two … Here we report the relationship between the two versions of the connectivity index for …
WebJul 6, 2024 · The topological indices exist in crisp but new to the fuzzy graph environment. This paper explains about the indices in fuzzy graph theory. In this paper, we discuss about new term definitions on Zagreb indices, Harmonic index, Randić index, Estrada index and Padmakar–Ivan index. Bounds for Zagreb indices are proved. christmas eve by janina tollikWebMar 18, 2015 · In this work, we present the minimum and maximum values of the harmonic index for unicyclic graphs with given girth, and characterize the corresponding extremal graphs. Skip to search form Skip to main content Skip to account menu. Semantic Scholar's Logo. Search 211,263,669 papers from all fields of science ... christmas eve bus times 2022WebFor a connected graph G G of order n n, the harmonic index of G G is the sum of weights 2 d(u)+d(v) 2 d ( u) + d ( v) over all edges uv u v of G G, where d(u) d ( u) and d(v) d ( v) … christmas eve by alistair cookeWebThe 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. christmas eve buffet menu recipesWebThe harmonic index of a graph G is defined as the sum of the 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 work, we present the minimum and… Expand 5 PDF Further Results on Harmonic Index and Some New Relations Between Harmonic Index and Other Topological Indices christmas eve bus timesWebApr 15, 2012 · The harmonic index H (G) of a graph G is defined as the sum of the weights all edges uv o G, where du denotes the degree o a vertex u in G. We compute the … gerold hirthWebJan 1, 2024 · The harmonic index of a graph G is defined as the sum of weights 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. A graph G ... christmas eve bus service