TY - CHAP

T1 - Fractional Dominating Parameters

AU - Goddard, Wayne

AU - Henning, Michael A.

N1 - Publisher Copyright:
© 2020, Springer Nature Switzerland AG.

PY - 2020

Y1 - 2020

N2 - For an arbitrary subset P of the reals and a graph G with vertex set V, a function f: V→ P is a P-dominating function of G if the sum of the function values over any closed neighborhood is at least 1. That is, for every v ∈ V, f(N[v]) ≥ 1. The P-domination number of a graph G is defined to be the infimum of f(V ) taken over all P-dominating functions f. When P= { 0, 1 } we obtain the standard domination number, and when P= { − 1, 0, 1 } or {−1, 1} we obtain the minus or signed domination number. In this chapter, we survey some results concerning fractional dominating parameters when P= [ 0, 1 ] or ℤ or ℝ in which case we obtain the fractional, integer, or real domination numbers, respectively.

AB - For an arbitrary subset P of the reals and a graph G with vertex set V, a function f: V→ P is a P-dominating function of G if the sum of the function values over any closed neighborhood is at least 1. That is, for every v ∈ V, f(N[v]) ≥ 1. The P-domination number of a graph G is defined to be the infimum of f(V ) taken over all P-dominating functions f. When P= { 0, 1 } we obtain the standard domination number, and when P= { − 1, 0, 1 } or {−1, 1} we obtain the minus or signed domination number. In this chapter, we survey some results concerning fractional dominating parameters when P= [ 0, 1 ] or ℤ or ℝ in which case we obtain the fractional, integer, or real domination numbers, respectively.

KW - Fractional domination

KW - Integer domination

KW - Real domination

UR - http://www.scopus.com/inward/record.url?scp=85093817705&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-51117-3_10

DO - 10.1007/978-3-030-51117-3_10

M3 - Chapter

AN - SCOPUS:85093817705

T3 - Developments in Mathematics

SP - 349

EP - 363

BT - Developments in Mathematics

PB - Springer

ER -