Journal of Guangxi Normal University(Natural Science Edition) ›› 2021, Vol. 39 ›› Issue (2): 112-118.doi: 10.16088/j.issn.1001-6600.2019062701

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Fractional Domination Numbers for Two Classes of Graphs

LI Guang, XU Baogen*, ZHANG Junxia   

  1. School of Science, East China Jiaotong University, Nanchang Jiangxi 330013, China
  • Received:2019-06-27 Revised:2019-10-11 Online:2021-03-25 Published:2021-04-15

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Abstract: Let G=(V,E) be a graph. A real-valued function f∶V→[0,1] is said to be a fractional dominating function (FDF) if f(N[u])≥1 holds for every vertex u∈V(G). The fractional domination number γf(G) of G is defined as γf(G)=min{f(V)|f is a FDF of graph G}. In this paper, the exact values of γf(Km×Pn),γ0f(Km×Pn) for all integers m≥3, n≥2, andγf(Km∨Pn) for all integers m≥5, n≥3 are given.

Key words: graph, product graph, join graph, fractional dominating function, fractional domination number

CLC Number: 

  • O157.5
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