78 research outputs found
New Results on Subtractive Magic Graphs
For any edge xy in a directed graph, the subtractive edge-weight is the sum of the label of xy and the label of y minus the label of x. Similarly, for any vertex z in a directed graph, the subtractive vertex-weight of z is the sum of the label of z and all edges directed into z and all the labels of edges that are directed away from z. A subtractive magic graph has every subtractive edge and vertex weight equal to some constant k. In this paper, we will discuss variations of subtractive magic labelings on directed graphs
SUPER (a,d)-EDGE ANTIMAGIC TOTAL LABELING OF CONNECTED TRIBUN GRAPH
Abstract. A G graph of order p and size q is called an (a,d)-edge antimagic total if there exist a bijection f:V(G)∪E(G)⟶{1,2,…,p+q} such that the edge-weights, w(uv)=f(u)+f(v)+f(uv), uv∈E(G), form an arithmetic sequence with first term a and common difference d. Such a graph G is called super if the smallest possible labels appear on the vertices. In this paper we study super (a, d)-edge-antimagic total properties of connected Tribun graph. The result shows that a connected Tribun graph admit a super(a,d)-edge antimagic total labeling ford=0,1,2 for n≥1. It can be concluded that the result of this research has covered all the feasible n,d. Key Words: (a,d)-edge antimagic vertex labeling, super(a,d)-edge antimagic total labeling, Tribun Graph.
Antimagic Labeling for Unions of Graphs with Many Three-Paths
Let be a graph with edges and let be a bijection from to
. For any vertex , denote by the sum of
over all edges incident to . If holds
for any two distinct vertices and , then is called an {\it antimagic
labeling} of . We call {\it antimagic} if such a labeling exists.
Hartsfield and Ringel in 1991 conjectured that all connected graphs except
are antimagic. Denote the disjoint union of graphs and by , and the disjoint union of copies of by . For an antimagic graph
(connected or disconnected), we define the parameter to be the
maximum integer such that is antimagic for all .
Chang, Chen, Li, and Pan showed that for all antimagic graphs , is
finite [Graphs and Combinatorics 37 (2021), 1065--1182]. Further, Shang, Lin,
Liaw [Util. Math. 97 (2015), 373--385] and Li [Master Thesis, National Chung
Hsing University, Taiwan, 2019] found the exact value of for special
families of graphs: star forests and balanced double stars respectively. They
did this by finding explicit antimagic labelings of and proving a
tight upper bound on for these special families. In the present
paper, we generalize their results by proving an upper bound on for
all graphs. For star forests and balanced double stars, this general bound is
equivalent to the bounds given in \cite{star forest} and \cite{double star} and
tight. In addition, we prove that the general bound is also tight for every
other graph we have studied, including an infinite family of jellyfish graphs,
cycles where , and the double triangle
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