TY - JOUR

T1 - Further results on total κ-subdominating functions in trees

AU - Harris, Laura M.

AU - Hattingh, Johannes H.

AU - Henning, Michael A.

N1 - Publisher Copyright:
© Copyright 2018, Charles Babbage Research Centre. All rights reserved.

PY - 2018/2

Y1 - 2018/2

N2 - A two-valued function f defined on the vertices of a graph G = (V, E), f: V → {-1,1} is an opinion function. For each vertex v of G, the vote of v is the sum of the function values of f over the open neighborhood of v. A total k-subdominating function (TkSF) of a graph G is an opinion function for which at least k of the vertices have a vote value of at least one. The total k-subdomination number, γkts(G), of G is the minimum value of f(V) over all TkSFs of G where f(V) denotes the sum of the function values assigned to the vertices under f. Trees of even order n achieving the maximum possible total k-subdomination number (namely, 2k - n) when n/2 ≤ k ≤ n/2 + 3 were characterized in [9]. Our aim in this paper is to characterize those trees of order n achieving the maximum possible total k-subdomination number (namely, 2k - n) when n is odd and (n + 3)/2 ≤ k ≤ (n + 5)/2.

AB - A two-valued function f defined on the vertices of a graph G = (V, E), f: V → {-1,1} is an opinion function. For each vertex v of G, the vote of v is the sum of the function values of f over the open neighborhood of v. A total k-subdominating function (TkSF) of a graph G is an opinion function for which at least k of the vertices have a vote value of at least one. The total k-subdomination number, γkts(G), of G is the minimum value of f(V) over all TkSFs of G where f(V) denotes the sum of the function values assigned to the vertices under f. Trees of even order n achieving the maximum possible total k-subdomination number (namely, 2k - n) when n/2 ≤ k ≤ n/2 + 3 were characterized in [9]. Our aim in this paper is to characterize those trees of order n achieving the maximum possible total k-subdomination number (namely, 2k - n) when n is odd and (n + 3)/2 ≤ k ≤ (n + 5)/2.

KW - Extremal

KW - Total k-subdomination

KW - Trees

UR - http://www.scopus.com/inward/record.url?scp=85045034041&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85045034041

SN - 0835-3026

VL - 104

SP - 65

EP - 73

JO - Journal of Combinatorial Mathematics and Combinatorial Computing

JF - Journal of Combinatorial Mathematics and Combinatorial Computing

ER -