ORIGINAL_ARTICLE
Totally magic cordial labeling of some graphs
A graph G is said to have a totally magic cordial labeling with constant C if there exists a mapping f : V (G) ∪ E(G) → {0, 1} such that f(a) + f(b) + f(ab) ≡ C (mod 2) for all ab ∈ E(G) and |nf (0) − nf (1)| ≤ 1, where nf (i) (i = 0, 1) is the sum of the number of vertices and edges with label i. In this paper, we give a necessary condition for an odd graph to be not totally magic cordial and also prove that some families of graphs admit totally magic cordial labeling.
https://jac.ut.ac.ir/article_7921_5e2b6a274667fa1b3976387dd2ecb005.pdf
2015-09-01
1
8
Cordial labeling
Totally magic cordial labeling
P.
Jeyanthi
jeyajeyanthi@rediffmail.com
1
2Research Center, Department of Mathematics, Aditanar College for women, Tiruchendur - 628 216, India
LEAD_AUTHOR
N.
Angel Benseera
2
Department of Mathematics, Sri enakshi Government Arts College for Women (Autonomous), Madurai - 625 002, India.
AUTHOR
ORIGINAL_ARTICLE
All Ramsey (2K2,C4)−Minimal Graphs
Let F, G and H be non-empty graphs. The notation F → (G,H) means that if any edge of F is colored by red or blue, then either the red subgraph of F con- tains a graph G or the blue subgraph of F contains a graph H. A graph F (without isolated vertices) is called a Ramsey (G,H)−minimal if F → (G,H) and for every e ∈ E(F), (F − e) 9 (G,H). The set of all Ramsey (G,H)−minimal graphs is denoted by R(G,H). In this paper, we characterize all graphs which are in R(2K2,C4).
https://jac.ut.ac.ir/article_7922_651e3bc41b32f240cb33e7a9669c32df.pdf
2015-11-25
9
25
Ramsey minimal graph
edge coloring
graph 2K2
cycle graph
Kristiana
Wijaya
kristiana.w@students.itb.ac.id
1
Combinatorial Mathematics Research Group, Faculty of Mathematics and natural Sciences, Institut Teknologi Bandung (ITB), Jalan Ganesa 10 Bandung 40132 Indonesia
LEAD_AUTHOR
Lyra
Yulianti
2
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Andalas University, Kampus UNAND Limau Manis Padang 25136 Indonesia
AUTHOR
Edy Tri
Baskoro
3
Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung (ITB), Jalan Ganesa 10 Bandung 40132 Indonesia
AUTHOR
Hilda
Assiyatun
hilda@math.itb.ac.id
4
Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung (ITB), Jalan Ganesa 10 Bandung 40132 Indonesia
AUTHOR
Djoko
Suprijanto
5
Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung (ITB), Jalan Ganesa 10 Bandung 40132 Indonesia
AUTHOR
ORIGINAL_ARTICLE
Vertex Equitable Labeling of Double Alternate Snake Graphs
Let G be a graph with p vertices and q edges and A = {0, 1, 2, . . . , [q/2]}. A vertex labeling f : V (G) → A induces an edge labeling f∗ defined by f∗(uv) = f(u) + f(v) for all edges uv. For a ∈ A, let vf (a) be the number of vertices v with f(v) = a. A graph G is said to be vertex equitable if there exists a vertex labeling f such that for all a and b in A, |vf (a) − vf (b)| ≤ 1 and the induced edge labels are 1, 2, 3, . . . , q. In this paper, we prove that DA(Tn)⊙K1, DA(Tn)⊙2K1(DA(Tn) denote double alternate triangular snake) and DA(Qn) ⊙ K1, DA(Qn) ⊙ 2K1(DA(Qn) denote double alternate quadrilateral snake) are vertex equitable graphs.
https://jac.ut.ac.ir/article_7923_76d1a6298f68c081c967627653edc287.pdf
2016-01-07
27
34
vertex equitable labeling
vertex equitable graph
double alternate triangular snake
double alternate quadrilateral snake
P.
Jeyanthi
jeyajeyanthi@rediffmail.com
1
1Research Center, Department of Mathematics, Govindammal Aditanar College for women, Tiruchendur - 628 215, Tamilnadu,India
LEAD_AUTHOR
A.
Maheswari
bala nithin@yahoo.co.in
2
2Department of Mathematics, Kamaraj College of Engineering and Technology, Virudhunagar, India
AUTHOR
M.
Vijayalakshmi
3
3Department of Mathematics, Dr.G.U. Pope College of Engineering, Sawyerpuram, Thoothukudi District, Tamilnadu, India
AUTHOR
ORIGINAL_ARTICLE
Mixed cycle-E-super magic decomposition of complete bipartite graphs
An H-magic labeling in a H-decomposable graph G is a bijection f : V (G) ∪ E(G) → {1, 2, ..., p + q} such that for every copy H in the decomposition, ∑νεV (H) f(v) + ∑νεE (H) f(e) is constant. f is said to be H-E-super magic if f(E(G)) = {1, 2, · · · , q}. A family of subgraphs H1,H2, · · · ,Hh of G is a mixed cycle-decomposition of G if every subgraph Hi is isomorphic to some cycle Ck, for k ≥ 3, E(Hi) ∩ E(Hj) = ∅ for i ≠ j and ∪hi=1E(Hi) = E(G). In this paper, we prove that K2m,2n is mixed cycle-E-super magic decomposable where m ≥ 2, n ≥ 3, with the help of the results found in [1].
https://jac.ut.ac.ir/article_7924_c5cc97b6cfd026d4c13e87b580a03b9a.pdf
2016-03-18
35
50
H-decomposable graph
H-E-super magic labeling
mixed cycle-E-super magic decomposable graph
G.
Marimuthu
yellowmuthu@yahoo.com
1
Department of Mathematics, The Madura College, Madurai -625 011, Tamilnadu, India
LEAD_AUTHOR
S.
Stalin Kumar
2
Department of Mathematics, The American College, Madurai -625 002, Tamilnadu,India
AUTHOR
ORIGINAL_ARTICLE
Toughness of the Networks with Maximum Connectivity
The stability of a communication network composed of processing nodes and communication links is of prime importance to network designers. As the network begins losing links or nodes, eventually there is a loss in its effectiveness. Thus, communication networks must be constructed to be as stable as possible, not only with respect to the initial disruption, but also with respect to the possible reconstruction of the network. For any fixed integers n,p with p ≥ n + 1, Harary constructed classes of graphs Hn,p that are n-connected with the minimum number of edges. Thus Harary graphs are examples of graphs with maximum connectivity. This property makes them useful to network designers and thus it is of interest to study the behavior of other stability parameters for the Harary graphs. In this paper we study the toughness of the third case of the Harary graphs.
https://jac.ut.ac.ir/article_7925_c2bbe11d39cad5af84f5731fc7c50217.pdf
2015-09-01
51
71
toughness
Harary graph
maximum connectivity
network
D.
Moazzami
dmoazzami@ut.ac.ir
1
University of Tehran, College of Engineering, Department of Engineering Science
LEAD_AUTHOR
ORIGINAL_ARTICLE
Further results on total mean cordial labeling of graphs
A graph G = (V,E) with p vertices and q edges is said to be a total mean cordial graph if there exists a function f : V (G) → {0, 1, 2} such that f(xy) = [(f(x)+f(y))/2] where x, y ∈ V (G), xy ∈ E(G), and the total number of 0, 1 and 2 are balanced. That is |evf (i) − evf (j)| ≤ 1, i, j ∈ {0, 1, 2} where evf (x) denotes the total number of vertices and edges labeled with x (x = 0, 1, 2). In this paper, we investigate the total mean cordial labeling of Cn2, ladder Ln, book Bm and some more graphs.
https://jac.ut.ac.ir/article_7926_9d2173db725a3759d46d6f1e33486b61.pdf
2015-09-01
73
83
cycle
Path
union of graphs
Star
ladder
R.
Ponraj
ponrajmaths@gmail.com
1
Department of Mathematics, Sri Paramakalyani College,Alwarkurichi-627 412, India
LEAD_AUTHOR
S.
Sathish Narayanan
2
Department of Mathematics, Sri Paramakalyani College,Alwarkurichi-627 412, India
AUTHOR