2017-12-16T22:14:47Z
http://jac.ut.ac.ir/?_action=export&rf=summon&issue=44
Journal of Algorithms and Computation
JAC
2776-2476
2776-2476
2015
46
1
Totally magic cordial labeling of some graphs
P.
Jeyanthi
N.
Angel Benseera
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.
Cordial labeling
Totally magic cordial labeling
2015
09
01
1
8
http://jac.ut.ac.ir/pdf_355_5e2b6a274667fa1b3976387dd2ecb005.html
Journal of Algorithms and Computation
JAC
2776-2476
2776-2476
2015
46
1
All Ramsey (2K2,C4)−Minimal Graphs
Kristiana
Wijaya
Lyra
Yulianti
Edy Tri
Baskoro
Hilda
Assiyatun
Djoko
Suprijanto
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).
Ramsey minimal graph
edge coloring
graph 2K2
cycle graph
2015
11
25
9
25
http://jac.ut.ac.ir/pdf_356_651e3bc41b32f240cb33e7a9669c32df.html
Journal of Algorithms and Computation
JAC
2776-2476
2776-2476
2015
46
1
Vertex Equitable Labeling of Double Alternate Snake Graphs
P.
Jeyanthi
A.
Maheswari
M.
Vijayalakshmi
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.
vertex equitable labeling
vertex equitable graph
double alternate triangular snake
double alternate quadrilateral snake
2016
01
07
27
34
http://jac.ut.ac.ir/pdf_357_76d1a6298f68c081c967627653edc287.html
Journal of Algorithms and Computation
JAC
2776-2476
2776-2476
2015
46
1
Mixed cycle-E-super magic decomposition of complete bipartite graphs
G.
Marimuthu
S.
Stalin Kumar
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].
H-decomposable graph
H-E-super magic labeling
mixed cycle-E-super magic decomposable graph
2016
03
18
35
50
http://jac.ut.ac.ir/pdf_358_c5cc97b6cfd026d4c13e87b580a03b9a.html
Journal of Algorithms and Computation
JAC
2776-2476
2776-2476
2015
46
1
Toughness of the Networks with Maximum Connectivity
D.
Moazzami
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.
toughness
Harary graph
maximum connectivity
Network
2015
09
01
51
71
http://jac.ut.ac.ir/pdf_359_c2bbe11d39cad5af84f5731fc7c50217.html
Journal of Algorithms and Computation
JAC
2776-2476
2776-2476
2015
46
1
Further results on total mean cordial labeling of graphs
R.
Ponraj
S.
Sathish Narayanan
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.
cycle
path
union of graphs
star
ladder
2015
09
01
73
83
http://jac.ut.ac.ir/pdf_360_9d2173db725a3759d46d6f1e33486b61.html