Roman domination number
Comparison of Roman Domination Number with Domination Number, Independent Domination Number and Chromatic Number of a Graph
... Proof: Roman Emperor Constantine had the requirement that an army or legion could be sent from its home to defend a neighboring location only if there was a second army, which would stay and protect the ...our ...
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Comparison of Efficient Domination Number with Domination Number, Roman Domination Number and Chromatic Number of a Graph
... Roman Emperor Constantine had the requirement that an army or legion could be sent from its home to defend a neighboring location only if there was a second army, which would stay and protect the ...our ...
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Classification Graphs with Large Strong Roman Domination Number
... domination number of a graph G which we denoted by SR G is minimum weight of an SRDF on G ...Strong Roman domination numbers 2 n 2 , 2 n 3 , 2 n 4 and 2 n 5 ...Strong ...
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Signed Roman Domination Number of Corona Graph CnKm
... Signed Roman dominating function of G, then we can see that among ‘m’ vertices of atmost vertices have functional value -1 and atleast one adjacent vertex of a vertex such that ( ) = −1 must have functional value ...
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More on Perfect Roman Domination in Graphs
... for which uv ∈ E(G). In other words, a P RD-function on G is a colouring of the vertices of G using colours 0, 1 and 2 such that each vertex coloured 0 is adjacent to exactly one vertex coloured 2. The perfect ...
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The Double Roman Domination Numbers of Generalized Petersen Graphs P(n, 2)
... In this paper we determine the exact value of the double Roman domination number of the generalized Petersen graphs P ( n , 2 ) by using a discharging approach.. Keywords: double Roman d[r] ...
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Roman Domination In An Interval Graph With Adjacent Cliques Of Size 3
... The Roman dominating function of a graph was defined by Cockayne ...a Roman dominating function was motivated by an article in Scientific American by Ian Stewart [4] entitled “Defend The Roman ...
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On Roman, Global and Restrained Domination in Graphs
... of Roman domination has its historical background and it can be used for the problems of this type, which arise in military and commercial decision ...the Roman domination number are ...
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Strong line domination in graphs
... independent domination number of a graph is the minimum cardinality of an independent dominating set (Haynes et ...split domination number of graph is the minimum cardinality of a strong split ...
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Complementary Tree Domination number and Distance two Complementary Tree Domination number of Cartesian Product of Graphs
... The concept of distance two complementary tree dominating set is introduced in [4]. A dominating set D is called a distance two complementary tree dominating set, if for each u ∈V(G) – D, there exists a vertex v ∈ D such ...
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Vol 10, No 6 (2019)
... p-domination number of graphs. Lu and Xu [8] gave the p-domination number of complete multipartite ...2-domination number of the corona of some ...2-domination ...
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Efficient Domination number and Chromatic number of a Fuzzy Graph
... a domination set in G if every vertex in V-S is adjacent to at least one vertex in ...total domination number and is denoted by (G). The minimum number of colours required to colour all the ...
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Total Domination Number and Chromatic Number of a Fuzzy Graph
... of domination in fuzzy graphs was investigated by ...independent domination, total domination, connected domination and domination in cartesian product and composition of fuzzy ...
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The k tuple domination number revisited
... double domination number was found by Harant and Henning [On double domination in ...triple domination number by Rautenbach and Volkmann [New bounds on the k-domination ...
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A Review on Lower Bounds for the Domination Number
... Equality holds in the bound above for cycles with orders congruent to 0 modulo 6. On the other hand, the tree obtained by algamating a pendant vertex to each vertex of a path has radius about n/3 while it has ...
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The Disjoint Total Domination Number of a Graph
... Abstract: The disjoint total domination number of a graph G is the minimum cardinality of the union of two disjoint total dominating sets in G. We also consider an invariant the minimum cardinality of the ...
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The Split Majority Domination Number of a Graph
... Definition 2.1. A majority dominating set D ⊆ V(G) is said to be split majority dominating set if the induced sub graph < V – D > is disconnected. A split majority dominating set D is minimal if no proper subset of ...
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On the k-Metro Domination Number of Paths
... Metro domination number introduced by Sooryanarayana and Raghunath [5]. Fink and Jacobson [6, 7] in 1985 introduced the concept of multiple domination. A subset D of V (G) is k-dominating in G if ...
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K - Domination Number of Butterfly Graphs
... We claim that D is a minimum 3-dominating set of BF(5). If possible let there be a 3-dominating set S such that │S│<│D. As the domination number of BF(n) is even, due to the symmetry of the graph, │S│ is ...
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On The K- Metro Domination Number of Cycle
... Metro Domination number introduced by B.Sooryanarayana, Raghunath. [5]. Fink and Ja-cobson [9] , [10] in 1985 introduced the concept of multiple domination. A subset D of V (G) is K- dominating in G ...
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