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A unified linear-programming modeling of some topological indices

Author

Listed:
  • Hanyuan Deng

    (Hunan Normal University)

  • Guihua Huang

    (Hunan Normal University)

  • Xiaojuan Jiang

    (Hunan Normal University)

Abstract

In this paper, we consider an invariant $$I(G)$$ I ( G ) of a graph $$G=(V,E)$$ G = ( V , E ) defined as a summation over all edges, $$I(G) = \sum {c_{ij}x_{ij}}$$ I ( G ) = ∑ c i j x i j where $$c_{ij}$$ c i j and $$x_{ij}$$ x i j is the weight and number, respectively, of edges in $$G$$ G connecting vertices of degree $$i$$ i and $$j$$ j . The graph invariant $$I(G)$$ I ( G ) unifies Randić index, Zagreb index, sum–connectivity index, $$GA_1$$ G A 1 index, ABC index and harmonic index. Based on linear programming methods, we give the extremal values and extremal graphs of $$I(G)$$ I ( G ) among all simple graphs of order $$n$$ n without isolated vertices. Applying this result, we obtain some extremal values of the Randić, Zagreb, sum–connectivity, $$GA_1$$ G A 1 , ABC, and harmonic indices along with the corresponding graphs that obtain these values.

Suggested Citation

  • Hanyuan Deng & Guihua Huang & Xiaojuan Jiang, 2015. "A unified linear-programming modeling of some topological indices," Journal of Combinatorial Optimization, Springer, vol. 30(3), pages 826-837, October.
    • Handle: RePEc:spr:jcomop:v:30:y:2015:i:3:d:10.1007_s10878-013-9672-2
    DOI: 10.1007/s10878-013-9672-2
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    Cited by:

    1. Chen, Hanlin & Wu, Renfang & Deng, Hanyuan, 2016. "The extremal values of some topological indices in bipartite graphs with a given matching number," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 103-109.

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