Total Labeling Research Articles

The Vertex and Edge Irregular Total Labeling of an Amalgamation of Two Isomorphic Cycles

The Vertex and Edge Irregular Total Labeling of an Amalgamation of Two Isomorphic Cycles

GRAF AJAIB TOTAL

A total labeling of a graph with p vertices and q edges is dened as a one-to-one map taking the vertices and edges onto the integers 1; 2; ; p + q. Such a labelingis vertex magic if the sum of the label on a vertex and the labels on its incident edgesis a constant independent of the choice of vertex, and edge magic if the sum of an edgelabel and the labels of the endpoints of the edge is constant. In this paper we examinegraphs possessing a labeling that is simultaneously vertex magic and edge magic. Suchgraphs appear to be rare.

On super (a,1)-edge-antimagic total labelings of cartesian product graphs

A graph G(V, E) with order p and size q is called (a,d)-edge-antimagic total if there exists a bijective function f : V(G) ⋃ E(G)→{1, 2, …, p + q} such that the edge-weights λf(uv) = f(u) + f(v) + f(uv), uv∊ E(G), form an arithmetic sequence with first term a and common difference d. Such a labeling is called super if the p smallest possible labels appear at the vertices. In this paper, we study super (a,1) -edge-antimagic properties of m (P2□Pn), m (P4□Pn) and m (C4□Pn) for m ≥ 1 and n ≥ 2.

Edge Coloring by Total Labelings of 4-regular Circulant Graphs

Abstract Edge-coloring total k-labeling of a connected graph G is an assignment f of non negative integers to the vertices and edges of G such that two adjacent edges e = u v and e ′ = u v ′ of G have different weights. The weight of an edge uv is defined by: w ( e = u v ) = f ( u ) + f ( v ) + f ( e ) . In this paper, we study the chromatic number of the edge coloring by total labeling of 4-regular circulant graphs C n ( 1 , k ) .

L( $$d$$ d ,1)-labelings of the edge-path-replacement by factorization of graphs

For an integer $$d \ge 2$$d?2, an $$L(d$$L(d,1)-labeling of a graph $$G$$G is a function $$f$$f from its vertex set to the non-negative integers such that $${\vert }f(x) - f(y){\vert } \ge d$$|f(x)?f(y)|?d if vertices $$x$$x and $$y$$y are adjacent, and $${\vert }f(x) - f(y){\vert } \ge $$|f(x)?f(y)|? 1 if $$x$$x and $$y$$y are at distance two. The minimum span over all the L($$d$$d,1)-labelings of $$G$$G is denoted by $$\lambda _{d}(G)$$?d(G). For a given integer $$k \ge 2$$k?2, the edge-path-replacement of$$G$$G or $$G(P_{k})$$G(Pk) is the graph obtained from $$G$$G by replacing each edge with a path $$P_{k}$$Pk on $$k$$k vertices. We show that the edges of $$G$$G can be colored with $$\lceil \varDelta (G)/2\rceil $$?Δ(G)/2? colors so that each monochromatic subgraph has maximum degree at most 2 and use this fact to establish general upper bounds on $$\lambda _{d}(G(P_{k}))$$?d(G(Pk)) for $$k \ge 4$$k?4. As a corollary, we settle the following conjecture by Lu (J Comb Optim, 2012): for any graph $$G$$G with $$\varDelta (G) \ge $$Δ(G)? 2, $$\lambda _{2}(G(P_{4})) \le \varDelta (G)$$?2(G(P4))≤Δ(G) + 2. Moreover, $$\lambda _{2}(G(P_{4})) = \varDelta (G) + 1$$?2(G(P4))=Δ(G)+1 when $$\varDelta (G)$$Δ(G) is even and different from 2. We also show that the class of graphs $$G(P_{k})$$G(Pk) with $$k \ge $$k? 4 satisfies a conjecture by Havet and Yu (2008 Discrete Math 308:498---513) in the related area of ($$d,1$$d,1)-total labeling of graphs.

PELABELAN TOTAL SISI AJAIB SUPER (TSAS) PADA GABUNGAN GRAF BINTANG GANDA DAN LINTASAN

An edge-magic total (EMT) labeling on a graph G(V,E) with the vertex set V and the edge set E , where | V| = p and |E| = q, is a bijective function λ : V E {1, 2, 3, ..., p + q} with the property that for each edge ( xy ) of G , λ(x) + λ(xy) + λ(y) = k , for a fixed positive integer k . The labeling λ is called a super edge magic total (SEMT) if it has the property that for each vertex obtain the smallest label, (V) = {1, 2, ..., p} . A graph G(V,E) is called EMT (SEMT) if there exists an EMT (SEMT) labeling on G . Study on SEMT labeling for the union of stars and paths initiated by Figueroa-Centeno et al. [2] with graph form . Furthermore, an investigation will be conducted on SEMT labeling of double stars and path, that are 2 ; 2 ; 2 and 2 . We obtain that the graphs presented above are SEMT with the magic constants k = , , and , respectively

Labels layout of cats and dogs food sold in Brazil and their national regulation adequacy

Due to the increasing of the pet foods marketing and the need to establish standards for quality and registration purposes, a study was conducted to evaluate the information on the package labels of 64 dogs and cats complete dry foods commercialized in Brazil and compare them to current regulation of the sector. From the total labels analyzed, all of them (100%) presented unconformity for at least one of the items evaluated. The highest rate of non-conformity was observed in the presentation of illustrations and phrases that induced the use of the product based on the false concept of advantage or animal health security (47%), leading to the misunderstanding of the owners. The results demonstrate a deficiency of the manufacturing companies regarding the labeling adequacy to the pet food regulation, as well as indicate a lack of rigorous enforcement by the agencies.

Further results on cycle-supermagic labeling

For a graph G(V, E), an edge-covering of G is a family of distinct subgraphs H1, … Hk such that any edge of E belongs to at least one of the subgraphs Hi, 1 ≤ k. If every Hi is isomorphic to a given graph H, then G admits an H-covering. Graph G is said to be H-magic if G has an H-covering and there is a total labeling f: V≼E → {1, 2,…, |V|+|E|} such that for each subgraph H' = (V', E') of G isomorphic to H, is a fixed constant. Furthermore, if f(V) = {1, 2,…,|V|} then G is called H-supermagic. The sum of all vertex and edge labels on H, under a labeling f, is denoted by Σf(H).In this paper we study H-supermagic labeling for some classes of graphs such as a Jahangir graph, a wheel graph for even n, and a complete bipartie graph Km,n for m = 2.

Wheel-supermagic labelings for a wheel k-multilevel corona with a cycle

Let k be a positive integer. A graph G k-multilevel corona with a graph H, denoted by G ⊙k H, is a graph that is defined by (G ⊙k-1 H) ⊙ H for k ≥ 2 and by G ⊙ H for k = 1 where G ⊙ H is a graph obtained from G and |V(G)| copies of H, namely H1, H2, …, H|V(G)|, and joined every vi in V(G) to all vertices in V(Hi). A graph G = (V,E) is said to be H -magic if every edge of G belongs to at least one subgraph isomorphic to H and there is a total labeling f: V(G)≼E(G) → {1, 2, …,|V(G)|+|E(G)|} such that for each subgraph H' = (V', E') of G isomorphic to H, the sum of all vertex labels in V' plus the sum of all edge labels in E' is a constant. Additionally, G is said to be H -supermagic, if f(V(G)) = {1, 2, …,|V(G)|}. We prove that a wheel Wn k-multilevel corona with a cycle Cn is Wn-supermagic.

On the total irregularity strength of some Cartesian product graphs

Let G = (V, E) be a graph. A total labeling f: V ≼ E → {1, 2,…, k} is called totally irregular total k-labeling of G if every two distinct vertices x and y in V satisfies wt(x) ≠ wt(y), and every two distinct edges x1x2 and y1 y2 in E satisfies wt(x1x2) ≠ wt(y1y2), where and wt(x1x2) = f(x1) + f(x1x2) + f(x2). The minimum k for which a graph G has a totally irregular total k-labeling is called the total irregularity strength of G, denoted by ts(G). The Cartesian product G□H of graphs G and H is a graph such that the vertex set of G□H is the Cartesian product V(G) x V(H) and any two vertices (u, u') and (v, v') are adjacent in G□H if and only if either u = v and u' is adjacent with v' in H, or u' = v' and u is adjacent with v in G. The join graph G+H of two graphs G and H is their graph union with all the edges that connect the vertices of G with the vertices of H. In this paper, we consider the total irregularity strength of some Cartesian product graphs, which are Sn□P2, (Pn+P1)□P2, Pn□P2, and Cn□P2, where Pn is a path of order n, Cn is a cycle of order n, and Sn is a star of order n+1.

Induced Total Labellings of Models as Scale-free Networks

A recently discovered approach including de Brujin graphs and Eulerian circuits are used to DNA sequencing and fragment assembly, and to simplify DNA graphs through a series of transformations on graphs and digraphs in the field of bioinformatics. Since numbered graphs provide underlying mathematical models in studying the wide variety of seemingly unrelated practical applications, so graph colorings often are used to divide large systems into subsystems. A new graph labeling has been introduced and investigated.

BEBERAPA SIFAT HIMPUNAN KRITIS PADA PELABELAN AJAIB GRAF BANANA TREE

A critical set in edge magic total labeling on graph G is a subset label such that it can forms the edge magic total labeling uniquely. This paper investigate critical set on Banana Tree graph. The result shows some properties of critical set on Banana Tree graph, such as the size of it at least , where n is number of leaf and k is number of star, except the size of critical set on graph BT(1,1) is 2. Beside it, if x is the label of any leaf and y is the label of the edge adjacent to it then each critical set in λ must contain either x or y, not both.

Edge Cordial, Total Edge Cordial Labeling Of Some Ladder Type Fractal Graphs

This paper deals with the concept of self-similarity fractals of four types of square ladder fractal with existence of Edge cordial labeling. A square graph is considered as base for square fractals which leads to construction of some of ladder type fractals. For our study each iterations and the generalized form are considered as graph. Eventually each graph is checked with edge cordial and total edge cordial labeling.

Supermagic coverings of the disjoint union of graphs and amalgamations

Let H be a graph. A graph G=(V,E) admits an H-covering if every edge in E belongs to a subgraph of G isomorphic to H. A graph G is called H-magic if there is a fixed integer k and a total labeling f:V∪E→{1,2,…,|V|+|E|} such that for each subgraph H′=(V′,E′) of G isomorphic to H, ∑v∈V′f(v)+∑e∈E′f(e)=k. If f(V)={1,2,…,|V|}, then G is H-supermagic. In this paper, we investigate the G-supermagicness of a disjoint union of c copies of a graph G. We characterize all such graphs of being G-supermagic. We also show that a disjoint union of any paths is cPh-supermagic for some c and h. Besides, we prove that certain subgraph-amalgamation of graphs G is G-supermagic.

Redox changes accompanying storage protein mobilization in moist chilled and warm incubated walnut kernels prior to germination

Alterations in the redox state of storage proteins and the associated proteolytic processes were investigated in moist-chilled and warm-incubated walnut (Juglans regia L.) kernels prior to germination. The kernel total protein labeling with a thiol-specific fluorochrome i.e. monobromobimane (mBBr) revealed more reduction of 29–32kDa putative glutelins, while in the soluble proteins, both putative glutelins and 41, 55 and 58kDa globulins contained reduced disulfide bonds during mobilization. Thus, the in vivo more reduced disulfide bonds of storage proteins corresponds to greater solubility. After the in vitro reduction of walnut kernel proteins pre-treated by N-ethyl maleimide (NEM) with dithioerythrethiol (DTT) and bacterial thioredoxin, the 58kDa putative globulin and a 6kDa putative albumin were identified as disulfide proteins. Thioredoxin stimulated the reduction of the H2O2-oxidized 6kDa polypeptide, but not the 58kDa polypeptide by DTT. The solubility of 6kDa putative albumin, 58 and 19–24kDa putative globulins and glutelins, respectively, were increased by DTT. The in vitro specific mobilization of the 58kDa polypeptide that occurred at pH 5.0 by the kernel endogenous protease was sensitive to the serine-protease inhibitor phenylmethylsulfonyl fluoride (PMSF) and stimulated by DTT. The specific degradation of the 58kDa polypeptide might be achieved through thioredoxin-mediated activation of a serine protease and/or reductive unfolding of its 58kDa polypeptide substrate. As redox changes in storage proteins occurred equally in both moist chilled and warm incubated walnut kernels, the regulatory functions of thioredoxins in promoting seed germination may be due to other germination related processes.

Cordial, Total Cordial, Edge Cordial, Total Edge Cordial Labeling of Some Box Type Fractal Graphs

This paper deals with the concept of self-similarity fractals of three types of box type fractal with existence of cordial and Edge cordial labeling. A square graph is considered as base for square fractals which leads to construction of some box type fractals. For our study each iteration and the generalized form are considered as graph. Eventually each graph is checked with cordial, edge cordial and total cordial, total edge cordial labeling.

Vertex-antimagic labelings of regular graphs

Let G = (V,E) be a finite, simple and undirected graph with p vertices and q edges. An (a, d)-vertex-antimagic total labeling of G is a bijection f from V (G) ∪ E(G) onto the set of consecutive integers 1, 2, …, p + q, such that the vertex-weights form an arithmetic progression with the initial term a and difference d, where the vertex-weight of x is the sum of the value f(x) assigned to the vertex x together with all values f(xy) assigned to edges xy incident to x. Such labeling is called super if the smallest possible labels appear on the vertices.

Formula omitted]-super vertex magic labelings of graphs

Let G be a finite simple graph with p vertices and q edges. A vertex magic total labeling is a bijection from V(G)∪E(G) to the consecutive integers 1,2,3,…,p+q with the property that for every u∈V(G),f(u)+∑v∈N(u)f(uv)=k for some constant k. Such a labeling isE-super if f(E(G))={1,2,3,…,q}. A graph G is called E-super vertex magic if it admits a E-super vertex magic labeling. In this paper, we study some basic properties of such labelings and we establish E-super vertex magic labeling of some families of graphs. The main focus of this paper is on the E-super vertex magicness of Hm,n and on some necessary conditions for a graph to be E-super vertex magic.

L(d,1)-labelings of the edge-path-replacement of a graph

For two positive integers j and k with j?k, an L(j,k)-labeling of a graph G is an assignment of nonnegative integers to V(G) such that the difference between labels of adjacent vertices is at least j, and the difference between labels of vertices that are distance two apart is at least k. The span of an L(j,k)-labeling of a graph G is the difference between the maximum and minimum integers used by it. The L(j,k)-labelings-number of G is the minimum span over all L(j,k)-labelings of G. This paper focuses on L(2,1)-labelings-number of the edge-path-replacement G(P k ) of a graph G. Note that G(P 3) is the incidence graph of G. L(2,1)-labelings of the edge-path-replacement G(P 3) of a graph, called (2,1)-total labeling of G, was introduced by Havet and Yu in 2002 (Workshop graphs and algorithms, Dijon, France, 2003; Discrete Math. 308:498---513, 2008). They (Havet and Yu, Discrete Math. 308:498---513, 2008) obtain the bound $\Delta+1\leq\lambda^{T}_{2}(G)\leq2\Delta+1$ and conjectured $\lambda^{T}_{2}(G)\leq\Delta+3$ . In this paper, we obtain that ?(G(P k ))?Δ+2 for k?5, and conjecture ?(G(P 4))?Δ+2 for any graph G with maximum degree Δ.

(p,q)-total labeling of complete graphs

Given a graph G and positive integers p,q with p≥q, the (p,q)-total number \(\lambda_{p,q}^{T}(G)\) of G is the width of the smallest range of integers that suffices to label the vertices and the edges of G such that the labels of any two adjacent vertices are at least q apart, the labels of any two adjacent edges are at least q apart, and the difference between the labels of a vertex and its incident edges is at least p. Havet and Yu (Discrete Math 308:496–513, 2008) first introduced this problem and determined the exact value of \(\lambda_{p,1}^{T}(K_{n})\) except for even n with p+5≤n≤6p2−10p+4. Their proof for showing that \(\lambda _{p,1}^{T}(K_{n})\leq n+2p-3\) for odd n has some mistakes. In this paper, we prove that if n is odd, then \(\lambda_{p}^{T}(K_{n})\leq n+2p-3\) if p=2, p=3, or \(4\lfloor\frac{p}{2}\rfloor+3\leq n\leq4p-1\). And we extend some results that were given in Havet and Yu (Discrete Math 308:496–513, 2008). Beside these, we give a lower bound for \(\lambda_{p,q}^{T}(K_{n})\) under the condition that q<p<2q.