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Information Journal Paper

Title

ROMAN GAME DOMINATION SUBDIVISION NUMBER OF A GRAPH

Pages

  1-12

Abstract

 A Roman dominating function on a graph G= (V, E) is a function f: V®{0, 1, 2} satisfying the condition that every vertex v for which f (v) =0 is adjacent to at least one vertex u for which f (u) =2. The weight of a Roman dominating function is the value w (f) = S vÎV f (v). The ROMAN DOMINATION NUMBER of a graph G, denoted by yR (G), equals the minimum weight of a Roman dominating function on G. The ROMAN GAME DOMINATION SUBDIVISION NUMBER of a graph G is defined by the following game. Two players D and A, D playing first, alternately mark or subdivide an edge of G which is not yet marked nor subdivided. The game ends when all the edges of G are marked or subdivided and results in a new graph G’. The purpose of D is to minimize the ROMAN DOMINATION NUMBER yR (G’) of G’ while A tries to maximize it. If both A and D play according to their optimal strategies, R (G0) is well defined. We call this number the ROMAN GAME DOMINATION SUBDIVISION NUMBER of G and denote it by yRgs (G). In this paper we initiate the study of the ROMAN GAME DOMINATION SUBDIVISION NUMBER of a graph and present sharp bounds on the ROMAN GAME DOMINATION SUBDIVISION NUMBER of a tree.

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    • Cite

    APA: Copy

    AMJADI, J., KARAMI, H., SHEIKHOLESLAMI, S.M., & VOLKMANN, L.. (2013). ROMAN GAME DOMINATION SUBDIVISION NUMBER OF A GRAPH. TRANSACTIONS ON COMBINATORICS, 2(4), 1-12. SID. https://sid.ir/paper/658403/en

    Vancouver: Copy

    AMJADI J., KARAMI H., SHEIKHOLESLAMI S.M., VOLKMANN L.. ROMAN GAME DOMINATION SUBDIVISION NUMBER OF A GRAPH. TRANSACTIONS ON COMBINATORICS[Internet]. 2013;2(4):1-12. Available from: https://sid.ir/paper/658403/en

    IEEE: Copy

    J. AMJADI, H. KARAMI, S.M. SHEIKHOLESLAMI, and L. VOLKMANN, “ROMAN GAME DOMINATION SUBDIVISION NUMBER OF A GRAPH,” TRANSACTIONS ON COMBINATORICS, vol. 2, no. 4, pp. 1–12, 2013, [Online]. Available: https://sid.ir/paper/658403/en

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