Preprint Article Version 1 This version is not peer-reviewed

The Double Roman Domination Numbers of Generalized Petersen Graphs P(n, 2)

Version 1 : Received: 18 July 2018 / Approved: 20 July 2018 / Online: 20 July 2018 (11:59:01 CEST)

How to cite: Jiang, H.; Wu, P.; Shao, Z.; Liu, J. The Double Roman Domination Numbers of Generalized Petersen Graphs P(n, 2). Preprints 2018, 2018070381 (doi: 10.20944/preprints201807.0381.v1). Jiang, H.; Wu, P.; Shao, Z.; Liu, J. The Double Roman Domination Numbers of Generalized Petersen Graphs P(n, 2). Preprints 2018, 2018070381 (doi: 10.20944/preprints201807.0381.v1).

Abstract

A double Roman dominating function on a graph G is a function f : V(G) → {0, 1, 2, 3} 2 with the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for 3 which f(v) = 3 or two vertices v1 and v2 for which f(v1) = f(v2) = 2, and every vertex u for which 4 f(u) = 1 is adjacent to at least one vertex v for which f(v) ≥ 2. The weight of a double Roman dominating function f is the value w(f) = ∑u∈V(G) 5 f(u). The minimum weight over all double 6 Roman dominating functions on a graph G is called the double Roman domination number γdR(G) 7 of G. In this paper we determine the exact value of the double Roman domination number of the 8 generalized Petersen graphs P(n, 2) by using a discharging approach.

Subject Areas

double Roman domination; discharging approach; generalized Petersen graphs

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