Degree series of the 3-harmonic graphs |
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| Authors: | Mu-huo Liu Bo-lian Liu |
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| Institution: | [1]Department of Mathematics, South China Agricultural University, Guangzhou 510642, China [2]School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China |
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| Abstract: | A λ harmonic graph G, a λ-Hgraph G for short, means that there exists a constant λ such that the equality λd(v
i
) =  holds for all i = 1, 2, …, |V(G)|, where d(v
i
) denotes the degree of vertex v
i
. Let n
i
denote the number of vertices with degree i. This paper deals with the 3-Hgraphs and determines their degree series. Moreover, the 3-Hgraphs with bounded n
i
(1 ≤ i ≤ 7) are studied and some interesting results are obtained.
The second author is the corresponding author who is supported by the National Natural Science Foundation of China (10771080)
and the Specialized Research Fund for the Doctoral Program of Higher Eduction (20070574006) |
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| Keywords: | harmonic graph non-regular graph degree series |
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