Let f : V (G) → {1, 2,..., |V (G)|} be a bijection, and let us denote S = f(u) + f(v) and D = |f(u) − f(v)| for every edge uv in E(G). Let f' be the induced edge labeling, induced by the vertex ...labeling f, defined as f' : E(G) → {0, 1} such that for any edge uv in E(G), f' (uv)=1 if gcd(S, D)=1, and f' (uv)=0 otherwise. Let ef' (0) and ef' (1) be the number of edges labeled with 0 and 1 respectively. f is SD-prime cordial labeling if |ef' (0) − ef' (1)| ≤ 1 and G is SD-prime cordial graph if it admits SD-prime cordial labeling. In this paper, we have discussed the SD-prime cordial labeling of alternate k-polygonal snake graphs of type-1, type-2 and type-3.
Here we discuss and prove that the graphs attained by switching of any vertex with degree two which is adjacent to a vertex with degree two in triangular snake T.sub.m, switching of any vertex with ...degree one in path P.sub.m for m greater than or equal to 3 and m odd, Switching of vertex with degree two in P.sub.m except vertices u.sub.2 or u.sub.m-1 with m > 4 and switching of any vertex in cycle C.sub.m are an edge product cordial graphs. Keywords: Graph labeling, Product cordial labeling, Switching Operation, Edge Product Cordial Labeling. AMS Subject Classification: 05C78.
The aim of the study was to outline a simple, cost-effective technique for obturation of primary tooth root canals. A total of 75 primary teeth were treated in 52 subjects by the technique discussed, ...i.e. injecting plastic flowable material into the root canals after desired preparation, using disposable needle and syringe. All the patients were followed up for 3 years and 6 months, with no clinical or radiologic evidence of pathology or need for untimely extraction. In conclusion, the technique described is simple, economical, can be used with almost all filling materials used for the purpose, and is easy to master with minimal chances of failure.
This study examines the probability of the degree splitting operation results from various graphs being product binary L-cordial Graphs. The graphs under investigation include the Path graph (Pn), ...Comb graph (Pn ⊙ k1), Double comb graph (Pn ⊙ 2k1), Cycle graph (Cn), Shell graph (Sn) and Ladder graph (Ln). The application of product binary L-cordial labeling demonstrates that these analyzed graphs exhibit characteristics of product binary L-cordial graphs.
Let f : V(G) right arrow {1, 2,... , |V(G)|} be a bijection, and let us denote S = f(u) + f(v) and D = |f(u) - f(v)| for every edge uv in E(G). Let f' be the induced edge labeling, induced by the ...vertex labeling f, defined as f' : E(G) right arrow {0,1} such that for any edge uv in E(G),f'(uv) = 1 if gcd(S, D) = 1, and f'(uv) = 0 otherwise. Let e.sub.f'/(0) and e.sub.f'/(1) be the number of edges labeled with 0 and 1 respectively. f is SD-prime cordial labeling if |e.sub.f'/(0) - e.sub.f'/(1)| less than or equal to 1 and G is SD-prime cordial graph if it admits SD-prime cordial labeling. In this paper, we have discussed the SD-prime cordial labeling of subdivision of K.sub.4--snake S(K.sub.4S.sub.n), subdivision of double K.sub.4--snake S(D(K.sub.4S.sub.n)), subdivision of alternate K.sub.4--snake S(A(K.sub.4S.sub.n)) of type 1, 2 and 3, and subdivision of double alternate K.sub.4--snake S(DA(K.sub.4S.sub.n)) of type 1, 2 and 3. Keywords: SD-prime cordial graph, Subdivision of K.sub.4--Snake, Subdivision of Alternate K.sub.4--Snake, Subdivision of Double K.sub.4--Snake, Subdivision of Double Alternate K.sub.4--Snake, m--Complete Snake. AMS Subject Classification: 05C78.
Let f : V (G) right arrow (1, 2,...,|V (G)|} be a bijection, and let us denote S = f (u) + f (v) and D = |f (u)-f (v)| for every edge uv in E(G). Let f' be the induced edge labeling, induced by the ...vertex labeling f, defined as f` : E(G) right arrow {0,1} such that for any edge uv in E(G),f`(uv) = 1 if gcd(S, D) = 1, and f` (uv) = 0 otherwise. Let e.sub.f`(0) and e.sub.f` (1) be the number of edges labeled with 0 and 1 respectively. f is SD-prime cordial labeling if |e.sub.f` (0)-e.sub.f` less than or equal to 1 and G is SD-prime cordial graph if it admits SD-prime cordial labeling. In this paper, we have discussed the SD-prime cordial labeling of subdivision of K.sub.4-snake S(K.sub.4S.sub.n), subdivision of double K.sub.4-snake S(D(K.sub.4S.sub.n)), subdivision of alternate K.sub.4-snake S(A(K.sub.4S.sub.n)) of type 1, 2 and 3, and subdivision of double alternate K.sub.4-snake S(DA(K.sub.4S.sub.n)) of type 1, 2 and 3. Keywords: SD-prime cordial graph, Subdivision of K.sub.4-Snake, Subdivision of Alternate K.sub.4-Snake, Subdivision of Double K.sub.4-Snake, Subdivision of Double Alternate K.sub.4-Snake, m-Complete Snake. AMS Subject Classification: 05C78.
Some Switching Invariant Prime Graphs Vaidya, S. K.; Prajapati, U. M.
Open journal of discrete mathematics,
2012, Letnik:
2, Številka:
1
Journal Article
Odprti dostop
We investigate prime labeling for some graphs resulted from switching of a vertex. We discuss switching invariance of some prime graphs and prove that the graphs obtained by switching of a vertex in ...Pn and K1,n admit prime labeling. Moreover we discuss prime labeling for the graph obtained by switching of vertex in wheel Wn.
Let G = (V(G),E(G)) be a graph and let f : V(G) → {0,1} be a mapping from the set of vertices to {0,1} and for each edge uv ∈ E assign the label |f (u) - f (v)|. If the number of vertices labeled ...with 0 and the number of vertices labeled with 1 differ by at most 1 and the number of edges labled with 0 and the number of edges labeled with 1 differ by at most 1, then f is called a cordial labeling. We discuss cordial labeling of graphs obtained from duplication of certain graph elements in web and armed helm.
PDF
