caa a22 4500 606244328 CHVBK 20210128101329.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s12044-015-0209-8 doi (NATIONALLICENCE)springer-10.1007/s12044-015-0209-8 Co-Roman domination in graphs [Elektronische Daten] [S ARUMUGAM, KARAM EBADI, MARTÍN MANRIQUE] Let G = (V,E) be a graph and let f : V → {0, 1, 2} be a function. A vertex u is said to be protected with respect to f if f(u) > 0 or f(u) = 0 and u is adjacent to a vertex with positive weight. The function f is a co-Roman dominating function (CRDF) if: (i) every vertex in V is protected, and (ii) each v ∈ V with f(v) > 0 has a neighbor u ∈ V with f(u) = 0 such that the function f vu : V → {0, 1, 2}, defined by f vu (u) = 1, f vu (v) = f(v) −1 and f vu (x) = f(x) for x ∈ V ∖ {u, v} has no unprotected vertex. The weight of f is w ( f ) = ∑ v ∈ V f ( v ) $w(f)={\sum }_{v\in V}f(v)$ . The co-Roman domination number of a graph G, denoted by γ c r (G), is the minimum weight of a co-Roman dominating function on G. In this paper we initiate a study of this parameter, present several basic results, as well as some applications and directions for further research. We also show that the decision problem for the co-Roman domination number is NP-complete, even when restricted to bipartite, chordal and planar graphs. Indian Academy of Sciences, 2015 Domination nationallicence Roman domination nationallicence weak Roman domination nationallicence co-Roman domination nationallicence ARUMUGAM S. National Centre for Advanced Research in Discrete Mathematics (n-CARDMATH), Kalasalingam University, Anand Nagar, 626 126, Krishnankoil, India aut EBADI KARAM National Centre for Advanced Research in Discrete Mathematics (n-CARDMATH), Kalasalingam University, Anand Nagar, 626 126, Krishnankoil, India aut MANRIQUE MARTÍN National Centre for Advanced Research in Discrete Mathematics (n-CARDMATH), Kalasalingam University, Anand Nagar, 626 126, Krishnankoil, India aut Proceedings - Mathematical Sciences Springer India 125/1(2015-02-01), 1-10 0253-4142 125:1<1 2015 125 12044 https://doi.org/10.1007/s12044-015-0209-8 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s12044-015-0209-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- ARUMUGAM S. National Centre for Advanced Research in Discrete Mathematics (n-CARDMATH), Kalasalingam University, Anand Nagar, 626 126, Krishnankoil, India aut NATIONALLICENCE 700 1- EBADI KARAM National Centre for Advanced Research in Discrete Mathematics (n-CARDMATH), Kalasalingam University, Anand Nagar, 626 126, Krishnankoil, India aut NATIONALLICENCE 700 1- MANRIQUE MARTÍN National Centre for Advanced Research in Discrete Mathematics (n-CARDMATH), Kalasalingam University, Anand Nagar, 626 126, Krishnankoil, India aut NATIONALLICENCE 773 0- Proceedings - Mathematical Sciences Springer India 125/1(2015-02-01), 1-10 0253-4142 125:1<1 2015 125 12044