2015
46
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0
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Totally magic cordial labeling of some graphs
2
2
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.
1

1
8


P.
Jeyanthi
2Research Center, Department of Mathematics, Aditanar College for women, Tiruchendur  628 216, India
2Research Center, Department of Mathematics,
Iran
jeyajeyanthi@rediffmail.com


N.
Angel Benseera
Department of Mathematics, Sri enakshi Government Arts College for Women (Autonomous), Madurai  625 002, India.
Department of Mathematics, Sri enakshi Government
Iran
Cordial labeling
Totally magic cordial labeling
All Ramsey (2K2,C4)−Minimal Graphs
2
2
Let F, G and H be nonempty 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).
1

9
25


Kristiana
Wijaya
Combinatorial Mathematics Research Group, Faculty of Mathematics and natural Sciences, Institut Teknologi Bandung (ITB), Jalan Ganesa 10 Bandung 40132 Indonesia
Combinatorial Mathematics Research Group,
Iran
kristiana.w@students.itb.ac.id


Lyra
Yulianti
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Andalas University, Kampus UNAND Limau Manis Padang 25136 Indonesia
Department of Mathematics, Faculty of Mathematics
Iran


Edy Tri
Baskoro
Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung (ITB), Jalan Ganesa 10 Bandung 40132 Indonesia
Combinatorial Mathematics Research Group,
Iran


Hilda
Assiyatun
Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung (ITB), Jalan Ganesa 10 Bandung 40132 Indonesia
Combinatorial Mathematics Research Group,
Iran
hilda@math.itb.ac.id


Djoko
Suprijanto
Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung (ITB), Jalan Ganesa 10 Bandung 40132 Indonesia
Combinatorial Mathematics Research Group,
Iran
Ramsey minimal graph
edge coloring
graph 2K2
cycle graph
Vertex Equitable Labeling of Double Alternate Snake Graphs
2
2
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.
1

27
34


P.
Jeyanthi
1Research Center, Department of Mathematics, Govindammal Aditanar College for women, Tiruchendur  628 215, Tamilnadu,India
1Research Center, Department of Mathematics,
Iran
jeyajeyanthi@rediffmail.com


A.
Maheswari
2Department of Mathematics, Kamaraj College of Engineering and Technology, Virudhunagar, India
2Department of Mathematics, Kamaraj College
Iran
bala nithin@yahoo.co.in


M.
Vijayalakshmi
3Department of Mathematics, Dr.G.U. Pope College of Engineering, Sawyerpuram, Thoothukudi District, Tamilnadu, India
3Department of Mathematics, Dr.G.U. Pope
Iran
vertex equitable labeling
vertex equitable graph
double alternate triangular snake
double alternate quadrilateral snake
Mixed cycleEsuper magic decomposition of complete bipartite graphs
2
2
An Hmagic labeling in a Hdecomposable 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 HEsuper magic if f(E(G)) = {1, 2, · · · , q}. A family of subgraphs H1,H2, · · · ,Hh of G is a mixed cycledecomposition 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 cycleEsuper magic decomposable where m ≥ 2, n ≥ 3, with the help of the results found in [1].
1

35
50


G.
Marimuthu
Department of Mathematics, The Madura College, Madurai 625 011, Tamilnadu, India
Department of Mathematics, The Madura College,
Iran
yellowmuthu@yahoo.com


S.
Stalin Kumar
Department of Mathematics, The American College, Madurai 625 002, Tamilnadu,India
Department of Mathematics, The American College,
Iran
Hdecomposable graph
HEsuper magic labeling
mixed cycleEsuper magic decomposable graph
Toughness of the Networks with Maximum Connectivity
2
2
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 nconnected 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.
1

51
71


D.
Moazzami
University of Tehran, College of Engineering, Department of Engineering Science
University of Tehran, College of Engineering,
Iran
dmoazzami@ut.ac.ir
toughness
Harary graph
maximum connectivity
Network
Further results on total mean cordial labeling of graphs
2
2
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.
1

73
83


R.
Ponraj
Department of Mathematics, Sri Paramakalyani College,Alwarkurichi627 412, India
Department of Mathematics, Sri Paramakalyani
Iran
ponrajmaths@gmail.com


S.
Sathish Narayanan
Department of Mathematics, Sri Paramakalyani College,Alwarkurichi627 412, India
Department of Mathematics, Sri Paramakalyani
Iran
cycle
path
union of graphs
star
ladder