Now showing items 1-20 of 26

    • Bound of Distance Domination Number of Graph and Edge Comb Product Graph 

      Gembong A.W; Slamin, Slamin; Dafik, Dafik; Agustin, Ika Hesti (2017-09-11)
      Let G =(V, E) be a simple, nontrivial, finite, connected and undirected graph. For an integer 1  k  diam(G), a distance k-dominating set of a connected graph G is a set S of vertices of G such that every vertex of V ...
    • The Connected and Disjoint Union of Semi Jahangir Graphs Admit a Cycle-Super (a, d)-Atimagic Total Labeling 

      Dafik, Dafik; Agustin, Ika Hesti; D. Hardiyantik (2018-02-28)
      We assume that all graphs in this paper are finite, undirected and no loop and multiple edges. Given a graph G of order p and size q.LetH ,H be subgraphs of G.ByH -covering, we mean every edge in E(G) belongs to at ...
    • The Construction of P2⊳H- antimagic graph using smaller edge - antimagic vertex labeling 

      Prihandini, Rafiantika Megahnia; Agustin, Ika Hesti; Dafik, Dafik (2018-07-04)
      In this paper we use simple and non trivial graph. If there exist a bijective function g : V (G) [ E(G) ! f1; 2; : : : ; jV (G)j + jE(G)jg, such that for all subgraphs P 2 B H of G isomorphic to H, then graph G is ...
    • Implementation of Super H-antimagic Total graph on Establishing Stream Cipher 

      Prihandoko, Antonius Cahya; Dafik, Dafik; Agustin, Ika Hesti (2019-07-12)
      This paper is aimed to study the use of super (a; d)-H antimagic total graph on generating en- cryption keys that can be used to establish a stream cipher. Methodology to achieve this goal was undertaken in three steps. ...
    • Local Edge Antimagic Coloring of Comb Product of Graphs 

      Agustin, Ika Hesti; Hasan, Mohammad; Dafik, Dafik; Alfarisi, Ridho; Kristiana, Arika Indah; Prihandini, Rafiantika Megahnia (2018-07-03)
      All graph in this paper are ¯nite, simple and connected graph. Let G(V; E) be a graph of vertex set V and edge set E. A bijection f : V (G) ¡! f1; 2; 3; :::; jV (G)jg is called a local edge antimagic labeling if for any ...
    • LOCAL EDGE ANTIMAGIC COLORING OF GRAPHS 

      Agustin, Ika Hesti; Hasan, Mohammad; Dafik, Dafik; Alfarisi, Ridho; Prihandini, Rafiantika Megahnia (2018-02-28)
      All graphs considered in this paper are finite, simple and connected graphs. Let G(V, E) be a graph with the vertex set V and the edge set E, and let w be the edge weight of graph G. Then a bijection f: V (G) → {1, 2, 3, ...
    • The Local Multiset Dimension of Graphs 

      Alfarisi, Ridho; Dafik, Dafik; Kristiana, Arika Indah; Agustin, Ika Hesti (2019-09-02)
      All graphs in this paper are nontrivial and connected graph. For 𝑘-ordered set 𝑊 = {𝑠1, 𝑠2, … , 𝑠𝑘} of vertex set 𝐺, the multiset representation of a vertex 𝑣 of 𝐺 with respect to 𝑊 is 𝑟𝑚(𝑣|𝑊) = ...
    • Non-Isolated Resolving Number of Graph with Pendant Edges 

      Alfarisi, Ridho; Dafik, Dafik; Kristiana, Arika Indah; Agustin, Ika Hesti (2019-07-25)
      We consider V; E are respectively vertex and edge sets of a simple, nontrivial and connected graph G. For an ordered set W = fw g of vertices and a vertex v 2 G, the ordered r(vjW) = (d(v; w 1 ); d(v; w 2 1 ; w 2 ; ...
    • The non-isolated resolving number of k-corona product of graphs 

      Alfarisi, Ridho; Dafik, Dafik; Slamin, Slamin; Agustin, Ika Hesti; Kristiana, Arika Indah (2018-07-04)
      Let all graphs be a connected and simple graph. A set W = fw g of veretx set of G, the kvector ordered r(vjW) = (d(x; w 1 ); d(x; w 2 1 ; w 2 ); : : : ; d(x; w )) of is a representation of v with respect to W, ...
    • On locating independent domination number of amalgamation graphs 

      Wardani, Dwi Agustin Retno; Dafik, Dafik; Agustin, Ika Hesti; Kurniawati, Elsa Yuli (2018-02-28)
      An independent set or stable set is a set of vertices in a graph in which no two of vertices are adjacent. A set D of vertices of graph G is called a dominating set if every vertex u 2 V (G) ¡ D is adjacent to some vertex ...
    • On r-dynamic coloring of some graph operations 

      Agustin, Ika Hesti; Dafik, Dafik; A.Y. Harsya (2018-03-07)
      Let G be a simple, connected and undirected graph. Given r; k as any natural numbers. By an r-dynamic k-coloring of graph G, we mean a proper k-coloring c(v) of G such that jc(N(v))j minfr; d(v)g for each vertex v in ...
    • On Rainbow k-Connection Number of Special Graphs and It's Sharp Lower Bound 

      Agustin, Ika Hesti; Dafik, Dafik; Gembong A.W (2018-02-28)
      Let G = (V; E) be a simple, nontrivial, nite, connected and undirected graph. Let c be a coloring c : E(G) ! f1; 2; : : : ; sg; s 2 N. A path of edge colored graph is said to be a rainbow path if no two edges on the ...
    • On Super Edge Local Antimagic Total Labeling by Using an Edge Antimagic Vertex Labeling Technique 

      Agustin, Ika Hesti; Dafik, Dafik; Marsidi, Marsidi; Alfarisi, Ridho; Kurniawati, Elsa Yuli (2019-07-25)
      In this paper, we consider that all graphs are finite, simple and connected. Let G(V,E) be a graph of vertex set V and edge set E. By a edge local antimagic total labeling, we mean a bijection f:V(G)∪E(G)→{1,2,3,...,|V(G)|+|E(G)|} ...
    • On The LDS of the Joint Product of Graphs 

      Agustin, Ika Hesti; Dafik, Dafik; Kusbudiono, Kusbudiono; Rachman, Shinta Aditya; Wardani, Dwi Agustin Retno (2019-09-02)
      Locating dominating set (LDS) is one of the topics of graph theory. A set VD of vertices in graph G is called a dominating set if every vertex V u is either an element of D or adjacent to some element ...
    • On the local edge antimagicness of m-splitting graphs 

      Albirri, Ermita Rizki; Dafik, Dafik; Slamin, Slamin; Agustin, Ika Hesti; Alfarisi, Ridho (2018-07-03)
      Let G be a connected and simple graph. A split graph is a graph derived by adding new vertex v 0 in every vertex v such that v 0 adjacent to v in graph G. An m-splitting graph is a graph which has m v 0 -vertices, ...
    • On The Local Metric Dimension of Line Graph of Special Graph 

      Marsidi, Marsidi; Dafik, Dafik; Agustin, Ika Hesti; Alfarisi, Ridho (2018-02-28)
      Let G be a simple, nontrivial, and connected graph. 𝑊 = {𝑤 } is a representation of an ordered set of k distinct vertices in a nontrivial connected graph G. The metric code of a vertex v, where 𝑣 ∈ G, the ordered ...
    • On the locating domination number of corona product 

      Santi, Risan Nur; Agustin, Ika Hesti; Dafik, Dafik; Alfarisi, Ridho (2018-07-04)
      Let G =(V (G),E(G) be a connected graph and v V (G). A dominating set for a graph G =(V, E) is a subset D of V such that every vertex not in D is adjacent to at least one member of D. The domination number γ(G) is the ...
    • On the total H-irregularity strength of graphs: A new notion 

      Agustin, Ika Hesti; Dafik, Dafik; Marsidi, Marsidi; Albirri, Ermita Rizki (2018-02-28)
      A total edge irregularity strength of G has been already widely studied in many papers. The total -labeling is said to be a total edge irregular -labeling of the graph G if for every two di erent edges e 1 and e 2 , ...
    • On the total rainbow connection of the wheel related graphs 

      M.S Hasan; Slamin, Slamin; Dafik, Dafik; Agustin, Ika Hesti; Alfarisi, Ridho (2018-07-04)
      Let G = (V (G); E(G)) be a nontrivial connected graph with an edge coloring c : E(G) ! f1; 2; :::; lg; l 2 N, with the condition that the adjacent edges may be colored by the same colors. A path P in G is called rainbow ...
    • P2 ▷ H-super antimagic total labeling of comb product of graphs 

      Agustin, Ika Hesti; Prihandini, Rafiantika Megahnia; Dafik, Dafik (2018-04-12)
      Let L and H be two simple, nontrivial and undirected graphs. Let o be a vertex of H, the comb product between L and H, denoted by L ▷ H, is a graph obtained by taking one copy of L and |V(L)| copies of H and grafting the ...