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1-edge balance index sets of C_n tines P_3 and K_{n,n}
Vinutha S . V.,Shrikanth A. S.,Ramananda H. S. 장전수학회 2019 Proceedings of the Jangjeon mathematical society Vol.22 No.3
Let G be a graph with vertex set V , edge set E and Z2 = {0, 1}. Let f be a labeling from E to Z2, so that the labels of the edges are 0 or 1. The edges labelled 1 are called 1-edges and edges labelled 0 are called 0-edges. The edge labeling f induces a vertex labeling f : V −! Z2 defined by f(v) = ( 1 if the number of 1-edges incident on v is odd, 0 if the number of 1-edges incident on v is even. For i 2 Z2 let ef (i) = e(i) = card{e 2 E : f(e) = i} and vf (i) = v(i) = card{v 2 V : f(v) = i}. A labeling f is said to be edge-friendly if | e(0) − e(1) | 1. The 1- edge balance index set (OEBI) of a graph G is defined by {| vf (0) − vf (1) | : the edge labeling f is edge-friendly}. The main purpose of this paper is to completely determine the 1-edge balance index sets of Cn × P3, Kn,n.
A note on Mycielskian type of a graph
C. Adiga,A. Bayad,A. S. Shrikanth 장전수학회 2012 Advanced Studies in Contemporary Mathematics Vol.22 No.1
In this paper we introduce and study an interesting graph transformation which we call the Mycielskian type graph of a graph. We show that MT(G), the Mycielskian type graph of a graph G has no k-fall coloring for any k >= 2. We also compute the spectrum of Mycielskian type graph of a k-regular graph G. Friendly index sets of Mycielskian type graphs of Pn and Cn are determined.
On Edge-balance Index Sets of N cycles Three Nested Graph (n = 0, 1, 2 (mod6))
Ying Wang,Yuge Zheng,C. ADIGA,Shrikanth A S 장전수학회 2011 Advanced Studies in Contemporary Mathematics Vol.21 No.1
Let G be a simple graph with vertex set V (G) and edge set E(G), and let Z_2 ={0, 1}. For a given binary labeling f : E(G) → Z_2, the edge labeling f induces a partial vertex labeling f^* : V (G) → Z_2 such that f^*(v) = 1(0) iff the number of 1-edges(0-edges) is strictly greater than the number of 0-edges(1-edges) incident to v, otherwise f^*(v) is not de¯ned. For i ∈ Z_2, let vf (i) = v(i) = card{v ∈V (G) : f^*(v) = i} and ef (i) = e(i) = card{e ∈ E(G) : f(e) = i}. The edge-balance index set of the graph G, EBI(G), is de¯ned as {|vf (0)-vf (1)| :the edge labeling f is edge-friendlyg. The graph C_n × P_3 is said that three cycles are linked with n paths. In this paper,we will research a structural method of the edge-balance index set of n cycles three nested graph (n≡0, 1, 2(mod6)).
Chandrashekar Adiga,E. Sampathkumar,M. A. Sriraj,Shrikanth A S 장전수학회 2013 Proceedings of the Jangjeon mathematical society Vol.16 No.3
In this paper, we introduce the concept of color energy of a graph, Ec(G) andcompute the color energy Ex(G) of few families of graphs with minimum number ofcolors. It depends on the underlying graph and colors on its vertices. We establishan upper bound and a lower bound for color energy. Also we introduce the conceptof complement of a colored graph and compute energies of complement of coloredgraphs of few families of graphs.
The role for GALNT14 in lung metastasis of breast cancer
Ki-Hoon Song,Mi So Park,Tulip S. Nandu,Shrikanth Gadad,Sang-Cheol Kim,Mi-Young Kim 한국당과학회 2018 한국당과학회 학술대회 Vol.2018 No.01
Polypeptide N-acetyl-galactosaminyltransferases (GALNTs) have been shown to play diverse roles in several biological processes, but their function in organ-tropic metastasis remains unknown. Here, we find that GALNT14expression is specifically associated with pulmonary metastasis in breast cancer patients. Furthermore, we demonstrate that GALNT14 promotes lung metastasis by facilitating two important steps during the metastatic process, i.e., initiation of metastatic colonies and their subsequent growth into overt metastases. Mechanistic studies suggest that GALNT14 not only augments self-renewal of breast cancer cells within the lung microenvironment but also allows breast cancer cells to exploit macrophage-derived growth factors for their continuous growth. The mediators of GALNT14 involved in these processes will also be discussed.