• Journal of applied mathematics & informatics
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• v.38 no.1_2
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• pp.189-200
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• 2020

Let G be a simple connected graph with n vertices and m edges. Denote by d₁ ≥ d₂ ≥ ⋯ ≥ d_n > 0 and d(e₁) ≥ d(e₂) ≥ ⋯ ≥ d(e_m) sequences of vertex and edge degrees, respectively. If vertices v_i and v_j are adjacent, we write i ~ j. The general sum-connectivity index is defined as 𝒳_α(G) = ∑_i~j(d_i + d_j)^α, where α is an arbitrary real number. Firstly, we determine a relation between 𝒳_α(G) and 𝒳_α-1(G). Then we use it to obtain some new bounds for 𝒳_α(G).

• Kyungpook Mathematical Journal
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• v.61 no.1
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• pp.61-74
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• 2021

Let G = (V, E) be a connected graph. The eccentric connectivity index of G is defined by ��C (G) = ∑u∈V (G) deg(u)e(u), where deg(u) and e(u) denote the degree and eccentricity of the vertex u in G, respectively. In this paper, we introduce a new formulation of ��C that will be called the distance eccentric connectivity index of G and defined by $${\xi}^{De}(G)\;=\;{\sum\limits_{u{\in}V(G)}}\;deg^{De}(u)e(u)$$ where degDe(u) denotes the distance eccentricity degree of the vertex u in G. The aim of this paper is to introduce and study this new topological index. The values of the eccentric connectivity index is calculated for some fundamental graph classes and also for some graph operations. Some inequalities giving upper and lower bounds for this index are obtained.

• Korean Journal of Environment and Ecology
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• v.26 no.2
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• pp.247-256
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• 2012

We evaluated the landscape ecological value of selected minefields and wetland patches as a habitat of the forest bird community. The avian fauna of three minefields of 8.5ha, 17.4ha, and 40.6ha were evaluated by comparing that of three control sites of mountain area. Average number of forest bird species, number of individuals, species diversity index, species richness, and species evenness were analyzed according to the size of patch and environmental characteristics such as the presence of wetland and connectivity. Community similarity was evaluated between test and control plots. Avian fauna can be summarized as follows. First, 63 species were recorded, and the sum of maximum counts was 828 individuals. Species diversity index was 3.8, and the species richness was 9.2. Species evenness was 93.3. Second, small, isolated forest patch had a low average number of species and individuals as expected. But, small forest patches with streams had higher bird density than patches without water surface. Third, forest patches with marsh wetland were evaluated as lower habitat quality than forest patches with stream wetland in terms of the number of bird species per unit area, number of individuals per unit area, species diversity index, species richness index, and species evenness. Finally, Community similarity of the small forest patches with streams was similar with large connected forest. As a result, lowland forest patch was shown the good quality for the forest bird community in spite of small extents, and community structure was similar with mountain forest bird community. Thus, riparian forest restoration could improve the biodiversity of the forest bird community.