SOLUTION TO THE MINIMUM HARMONIC INDEX OF GRAPHS WITH GIVEN MINIMUM DEGREE

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LIANG MEILI; CHENG BO; LIU JIANXI

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Paper Information

Journal: TRANSACTIONS ON COMBINATORICS Year:2018 | Volume:7 | Issue:2 Page(s): 25-33

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Title

SOLUTION TO THE MINIMUM HARMONIC INDEX OF GRAPHS WITH GIVEN MINIMUM DEGREE

Author(s)

LIANG MEILI | CHENG BO | LIU JIANXI | Issue Writer Certificate

Keywords

HARMONIC INDEX

MINIMUM DEGREE

EXTREMAL GRAPHS

Abstract

The HARMONIC INDEX of a graph G is dened as H (G) =å uuÎE(G) 2 d(u)+d (u), where d (u) denotes the degree of a vertexu in G. Let G (n; k) be the set of simple n -vertex graphs with MINIMUM DEGREE at leastk. In this work we consider the problem of determining the minimum value of the HARMONIC INDEX and the corresponding EXTREMAL GRAPHS among G (n; k). We solve the problem for each integerk (1 £ k £ n/2) and show the corresponding extremal graph is the complete split graph K *k, n-k. This result together with our previous result which solve the problem for each integer k (n/2 £ k £ n - 1) give a complete solution of the problem.

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APA: Copy

LIANG, MEILI, CHENG, BO, & LIU, JIANXI. (2018). SOLUTION TO THE MINIMUM HARMONIC INDEX OF GRAPHS WITH GIVEN MINIMUM DEGREE. TRANSACTIONS ON COMBINATORICS, 7(2), 25-33. SID. https://sid.ir/paper/712117/en

Vancouver: Copy

LIANG MEILI, CHENG BO, LIU JIANXI. SOLUTION TO THE MINIMUM HARMONIC INDEX OF GRAPHS WITH GIVEN MINIMUM DEGREE. TRANSACTIONS ON COMBINATORICS[Internet]. 2018;7(2):25-33. Available from: https://sid.ir/paper/712117/en

IEEE: Copy

MEILI LIANG, BO CHENG, and JIANXI LIU, “SOLUTION TO THE MINIMUM HARMONIC INDEX OF GRAPHS WITH GIVEN MINIMUM DEGREE,” TRANSACTIONS ON COMBINATORICS, vol. 7, no. 2, pp. 25–33, 2018, [Online]. Available: https://sid.ir/paper/712117/en

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