Indonesian Journal of Combinatorics最新文献

 Let G be a finite group and let N be a fixed normal subgroup of G.  In this paper, a new kind of graph on G, namely the intersection graph is defined and studied. We use  to denote this graph, with its vertices are all normal subgroups of G and two distinct vertices are adjacent if their intersection in N. We show some properties of this graph. For instance, the intersection graph is a simple connected with diameter at most two. Furthermore we give the graph structure of  for some finite groups such as the symmetric, dihedral, special linear group, quaternion and cyclic groups. 

Characterizing all graphs having a certain locating-chromatic number is not an easy task. In this paper, we are going to pay attention on finding all unicyclic graphs of order n (⩾ 6) and having locating-chromatic number n-3.

An edge irregular total k-labeling f : V ∪ E → 1,2, ..., k of a graph G = (V,E) is a labeling of vertices and edges of G in such a way that for any two different edges uv and u'v', their weights f(u)+f(uv)+f(v) and f(u')+f(u'v')+f(v') are distinct. The total edge irregularity strength tes(G) is defined as the minimum k for which the graph G has an edge irregular total k-labeling. In this paper, we determine the total edge irregularity strength of new classes of graphs C_m @ C_n, P_m,n* and C_m,n* and hence we extend the validity of the conjecture tes(G) = max {⌈|E(G)|+2)/3⌉, ⌈(Δ(G)+1)/2⌉}  for some more graphs.

Let G(V,E) be a simple and connected graph which set of vertices is V and set of edges is E. Irregular reflexive k-labeling f on G(V,E) is assignment that carries the numbers of integer to elements of graph, such that the positive integer {1,2, 3,...,k_e} assignment to edges of graph and the even positive integer {0,2,4,...,2k_v} assignment to vertices of graph. Then, we called as edge irregular reflexive k-labelling if every edges has different weight with k = max{k_e,2k_v}. Besides that, there is definition of reflexive edge strength of G(V,E) denoted as res(G), that is a minimum k that using for labeling f on G(V,E). This paper will discuss about edge irregular reflexive k-labeling for sun graph and corona of cycle and null graph, denoted by C_n ⨀ N₂ and make sure about their reflexive edge strengths.

A set D - V is a dominating set of G if every vertex in V - D is adjacent to some vertex in D. The dominating number γ(G) of G is the minimum cardinality of a dominating set D. A dominating set D of a graph G = (V;E) is a split dominating set if the induced graph (V - D) is disconnected. The split domination number γ_s(G) is the minimum cardinality of a split domination set. In this paper we have introduced a new method to obtain the split domination number of grid graphs by partitioning the vertex set in terms of star graphs and also we have
obtained the exact values of γs(G_m;n); m ≤ n; m,n ≤ 24:

For a connected graph G = (V, E), let a set S be a m-set of G. A subset T ⊆ S is called a forcing subset for S if S is the unique m-set containing T. A forcing subset for S of minimum cardinality is a minimum forcing subset of S. The forcing monophonic number of S, denoted by fm(S), is the cardinality of a minimum forcing subset of S. The forcing monophonic number of G, denoted by fm(G), is fm(G) = min{fm(S)}, where the minimum is taken over all minimum monophonic sets in G. We know that m(G) ≤ g(G), where m(G) and g(G) are monophonic number and geodetic number of a connected graph G respectively. However there is no relationship between fm(G) and fg(G), where fg(G) is the forcing geodetic number of a connected graph G. We give a series of realization results for various possibilities of these four parameters.