Browsing by Author "Durgun D.D."

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    Packing chromatic number of transformation graphs
    (Serbian Society of Heat Transfer Engineers, 2019) Durgun D.D.; Ozen Dortok H.B.
    Graph coloring is an assignment of labels called colors to elements of a graph. The packing coloring was introduced by Goddard et al. [1] in 2008 which is a kind of coloring of a graph. This problem is NP-complete for general graphs. In this paper, we consider some transformation graphs and generalized their packing chromatic numbers. © 2019 Society of Thermal Engineers of Serbia.
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    Weak and strong domination in thorn graphs
    (World Scientific Publishing Co. Pte Ltd, 2020) Durgun D.D.; Lökçü B.
    Let G = (V,E) be a graph and u,v V. A dominating set D is a set of vertices such that each vertex of G is either in D or has at least one neighbor in D. The minimum cardinality of such a set is called the domination number of G, γ(G). u strongly dominates v and v weakly dominates u if (i) uv E and (ii) deg u ≥deg v. A set D V is a strong-dominating set, shortly sd-set, (weak-dominating set, shortly wd-set) of G if every vertex in V-D is strongly (weakly) dominated by at least one vertex in D. The strong (weak) domination number γs(γw) of G is the minimum cardinality of an sd-set (wd-set). In this paper, we present weak and strong domination numbers of thorn graphs. © 2020 World Scientific Publishing Company.
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    Weak and strong domination on some graphs
    (EDP Sciences, 2022) Durgun D.D.; Kurt B.L.
    Let G = (V(G), E(G)) be a graph and uv?E. A subset D âV of vertices is a dominating set if every vertex in V-D is adjacent to at least one vertex of D. The domination number is the minimum cardinality of a dominating set. Let u and v be elements of V. Then, u strongly dominates u and v weakly dominates u if (i)uv?E and (ii)deg(u) ?deg(v). A set D â V is a strong (weak) dominating set (sd-set)(wd-set) of G if every vertex in V-D is strongly dominated by at least one vertex in D. The strong (weak) domination number ?s(?w) of G is the minimum cardinality of a sd-set (wd-set). In this paper, the strong and weak domination numbers of comet, double comet, double star and theta graphs are given. The theta graphs are important geometric graphs that have many applications, including wireless networking, motion planning, MST construction and real-Time animation. © The authors.