Here we show that graphs constructed by edge comb product of path Pn and cycle on four vertices C4 or shadow of cycle of order four D2(C4) are odd harmonious.
Here we show that graphs constructed by edge comb product of path Pn and cycle on four vertices C4 or shadow of cycle of order four D2(C4) are odd harmonious.
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 Cm @ Cn, Pm,n* and Cm,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,...,ke} assignment to edges of graph and the even positive integer {0,2,4,...,2kv} assignment to vertices of graph. Then, we called as edge irregular reflexive k-labelling if every edges has different weight with k = max{ke,2kv}. 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 Cn ⨀ 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 γs(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(Gm;n); m ≤ n; m,n ≤ 24:
Under a totally irregular total k-labeling of a graph G = (V,E), we found that for some certain graphs, the edge-weight set W(E) and the vertex-weight set W(V) of G which are induced by k = ts(G), W(E) ∩ W(V) is a non empty set. For which k, a graph G has a totally irregular total labeling if W(E) ∩ W(V) = ∅? We introduce the total disjoint irregularity strength, denoted by ds(G), as the minimum value k where this condition satisfied. We provide the lower bound of ds(G) and determine the total disjoint irregularity strength of cycles, paths, stars, and complete graphs.
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：