Edge Uv Research Articles

Pair difference cordial labeling of graphs

Let G = (V,E) be a (p,q) graph. Define ρ = p/2, if p is even; (p−1)/2, if p is odd; and L = {±1,±2,±3,··· ,±ρ} called the set of labels. Consider a mapping f: V → L by assigning different labels in L to the different elements of V when p is even and different labels in L to p-1 elements of V and repeating a label for the remaining one vertex when p is odd. The labeling as defined above is said to be a pair difference cordial labeling if for each edge uv of G there exists a labeling |f(u)− f(v)| such that |∆f1 −∆f 1 c | ≤ 1, where ∆f 1 and ∆f 1 c respectively denote the number of edges labeled with 1 and number of edges not labeled with 1. A graph G for which there exists a pair difference cordial labeling is called a pair difference cordial graph. In this paper we investigate the pair difference cordial labeling behavior of path, cycle, star, comb.

Further results on super graceful labeling of graphs

Further results on super graceful labeling of graphs

On irreducible no-hole L(2, 1)-coloring of subdivision of graphs

An L(2, 1)-coloring (or labeling) of a graph G is a mapping $$f:V(G) \rightarrow \mathbb {Z}^{+}\bigcup \{0\}$$f:V(G)źZ+ź{0} such that $$|f(u)-f(v)|\ge 2$$|f(u)-f(v)|ź2 for all edges uv of G, and $$|f(u)-f(v)|\ge 1$$|f(u)-f(v)|ź1 if u and v are at distance two in G. The span of anL(2, 1)-coloringf, denoted by span f, is the largest integer assigned by f to some vertex of the graph. The span of a graphG, denoted by $$\lambda (G)$$ź(G), is min {span $$f: f\text {is an }L(2,1)\text {-coloring of } G\}$$f:fis anL(2,1)-coloring ofG}. If f is an L(2, 1)-coloring of a graph G with span k then an integer l is a hole in f, if $$l\in (0,k)$$lź(0,k) and there is no vertex v in G such that $$f(v)=l$$f(v)=l. A no-hole coloring is defined to be an L(2, 1)-coloring with span k which uses all the colors from $$\{0,1,\ldots ,k\}$${0,1,ź,k}, for some integer k not necessarily the span of the graph. An L(2, 1)-coloring is said to be irreducible if colors of no vertices in the graph can be decreased and yield another L(2, 1)-coloring of the same graph. An irreducible no-hole coloring of a graph G, also called inh-coloring of G, is an L(2, 1)-coloring of G which is both irreducible and no-hole. The lower inh-span or simply inh-span of a graph G, denoted by $$\lambda _{inh}(G)$$źinh(G), is defined as $$\lambda _{inh}(G)=\min ~\{$$źinh(G)=min{span f : f is an inh-coloring of G}. Given a graph G and a function h from E(G) to $$\mathbb {N}$$N, the h-subdivision of G, denoted by $$G_{(h)}$$G(h), is the graph obtained from G by replacing each edge uv in G with a path of length h(uv). In this paper we show that $$G_{(h)}$$G(h) is inh-colorable for $$h(e)\ge 2$$h(e)ź2, $$e\in E(G)$$eźE(G), except the case $$\Delta =3$$Δ=3 and $$h(e)=2$$h(e)=2 for at least one edge but not for all. Moreover we find the exact value of $$\lambda _{inh}(G_{(h)})$$źinh(G(h)) in several cases and give upper bounds of the same in the remaining.

A note on the neighbor sum distinguishing total coloring of planar graphs

A note on the neighbor sum distinguishing total coloring of planar graphs

K-PRIME CORDIAL GRAPHS

In this paper we introduce a new graph labeling called k-prime cordial labeling. Let G be a (p, q) graph and 2 ≤ p ≤ k. Let f : V (G) → {1, 2, . . . , k} be a map. For each edge uv, assign the label gcd (f(u), f(v)). f is called a k-prime cordial labeling of G if |v_f (i) − v_f (j)| ≤ 1, i, j ∈ {1, 2, . . . , k} and |e_f (0) − e_f (1)| ≤ 1 where v_f (x) denotes the number of vertices labeled with x, e_f (1) and e_f (0) respectively denote the number of edges labeled with 1 and not labeled with 1. A graph with a k-prime cordial labeling is called a k-prime cordial graph. In this paper we investigate the k-prime cordial labeling behavior of a star and we have proved that every graph is a subgraph of a k-prime cordial graph. Also we investigate the 3-prime cordial labeling behavior of path, cycle, complete graph, wheel, comb and some more standard graphs.

Influence of Cu doping on structural, morphological, photoluminescence, and electrical properties of ZnO nanostructures synthesized by ice-bath assisted sonochemical method

Influence of Cu doping on structural, morphological, photoluminescence, and electrical properties of ZnO nanostructures synthesized by ice-bath assisted sonochemical method

Neighbor distinguishing total choice number of sparse graphs via the Combinatorial Nullstellensatz

Let G = (V,E) be a graph and ϕ: V ∪E → {1, 2, · · ·, k} be a total-k-coloring of G. Let f(v)(S(v)) denote the sum(set) of the color of vertex v and the colors of the edges incident with v. The total coloring ϕ is called neighbor sum distinguishing if (f(u) ≠ f(v)) for each edge uv ∈ E(G). We say that ϕ is neighbor set distinguishing or adjacent vertex distinguishing if S(u) ≠ S(v) for each edge uv ∈ E(G). For both problems, we have conjectures that such colorings exist for any graph G if k ≥ Δ(G) + 3. The maximum average degree of G is the maximum of the average degree of its non-empty subgraphs, which is denoted by mad (G). In this paper, by using the Combinatorial Nullstellensatz and the discharging method, we prove that these two conjectures hold for sparse graphs in their list versions. More precisely, we prove that every graph G with maximum degree Δ(G) and maximum average degree mad(G) has chΣ″(G) ≤ Δ(G) + 3 (where chΣ″(G) is the neighbor sum distinguishing total choice number of G) if there exists a pair \((k,m) \in \{ (6,4),(5,\tfrac{{18}} {5}),(4,\tfrac{{16}} {5})\}\) such that Δ(G) ≥ k and mad (G) <m.

ON SD-PRIME CORDIAL GRAPHS

Let G = (V (G),E(G)) be a simple, finite and undirected graph of order n. Given a bijection f : V (G) → {1,...,n}, we associate 2 integers S = f(u) + f(v) and D = |f(u) − f(v)| with every edge uv in E(G). The labeling f induces an edge labeling 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'(i) be the number of edges labeled with i ∈ {0,1}. We say f is an SD-prime cordial labeling if |ef'(0) − ef'(1)| ≤ 1. Moreover G is SD-prime cordial if it admits an SD-prime cordial labeling. In this paper, we investigate the SD-prime cordiality of some standard graphs.

The adjacent vertex distinguishing total coloring of planar graphs without adjacent 4-cycles

A total [k]-coloring of a graph G is a mapping $$\phi $$ź: $$V(G)\cup E(G)\rightarrow [k]=\{1, 2,\ldots , k\}$$V(G)źE(G)ź[k]={1,2,ź,k} such that no two adjacent or incident elements in $$V(G)\cup E(G)$$V(G)źE(G) receive the same color. In a total [k]-coloring $$\phi $$ź of G, let $$C_{\phi }(v)$$Cź(v) denote the set of colors of the edges incident to v and the color of v. If for each edge uv, $$C_{\phi }(u)\ne C_{\phi }(v)$$Cź(u)źCź(v), we call such a total [k]-coloring an adjacent vertex distinguishing total coloring of G. $$\chi ''_{a}(G)$$źaźź(G) denotes the smallest value k in such a coloring of G. In this paper, by using the Combinatorial Nullstellensatz and the discharging method, we prove that if a planar graph G with maximum degree $$\Delta \ge 8$$Δź8 contains no adjacent 4-cycles, then $$\chi ''_{a}(G)\le \Delta +3$$źaźź(G)≤Δ+3.

Neighbor sum distinguishing total choosability of planar graphs without 4-cycles

Neighbor sum distinguishing total choosability of planar graphs without 4-cycles

Morphological evolution of hydrothermally derived ZnO nano and microstructures

Morphological evolution of hydrothermally derived ZnO nano and microstructures

Cube Divisor Cordial Labeling of some Standard Graphs

The present authors are motivated by two research articles Di- visor Cordial Graphs by Varatharajan et al. and Square Divisor Cordial Graphs by Murugesan et al. We introduce the concept of cube divisor cor- dial labeling. A cube divisor cordial labeling of a graph G with vertex set V is a bijection f from V to {1, 2,…,|v|} such that an edge uv is assigned the label 1 if [f(u)] 3 |f(v) or [f(v)] 3 |f(u) and the label 0 otherwise, then |e f (0) -e f (1)| ≤ 1. A graph which admits a cube divisor cordial labeling is called a cube divisor cordial graph . In this paper we discuss cube divisor cordial labeling of some standard graphs such as path, cycle, wheel, flower and fan.

Enhanced UV–vis photoconductivity and photoluminescence by doping of samarium in ZnO nanostructures synthesized by solid state reaction method

Enhanced UV–vis photoconductivity and photoluminescence by doping of samarium in ZnO nanostructures synthesized by solid state reaction method

Duplication and Switching of Divisor Cordial Graphs

Duplication and Switching of Divisor Cordial Graphs P. Maya, T. Nicholas Abstract A divisor cordial labeling of a graph G with vertex set V is a bijection f from V to {1, 2, 3, . . .,|V|} such that if an edge uv is assigned the label 1 if f(u) divides f(v) or f(v) divides f(u) and 0 otherwise, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. If a graph has a divisor cordial labeling, then it is called divisor cordial graph. In this paper, we prove that fan graph, switching of a pendant vertex of a helm graph, switching of a vertex of flower graph, switching of closed helm graph, and also duplication of an arbitrary vertex by an edge of a fan graph are divisor cordial. Full Text: PDF DOI: 10.15640/arms.v4n2a3

Inapproximability of the lid-chromatic number

Inapproximability of the lid-chromatic number

Kings and Heirs: A characterization of the [formula omitted]-domination graphs of tournaments

Kings and Heirs: A characterization of the [formula omitted]-domination graphs of tournaments

An edge-rotating theorem on the least eigenvalue of graphs

Let G = (V (G), E(G)) be a simple connected graph of order n. For any vertices u, v,w ∈ V (G) with uv ∈ E(G) and uw ∈ E(G), an edge-rotating of G means rotating the edge uv (around u) to the non-edge position uw. In this work, we consider how the least eigenvalue of a graph perturbs when the graph is performed by rotating an edge from the shorter hanging path to the longer one.

TREE RELATED EXTENDED MEAN CORDIAL GRAPHS

Let G = (V,E) be a graph with p vertices and q edges. A Extended Mean Cordial Labeling of a Graph G with vertex set V is a bijection from V to {0, 1,2} such that each edge uv is assigned the label where ⌈ x ⌉ is the least integer greater than or equal to x with the condition that 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 labeled with 0 and the number of edges labeled with 1 differ by almost 1. The graph that admits an Extended Mean Cordial Labeling is called Extended Mean Cordial Graph. In this paper, we proved that tree related graphs Hdn, K 1,n, Tgn, &lt;K1,n:n&gt; are Extended Mean Cordial Graphs.

On the neighbor sum distinguishing total coloring of planar graphs

On the neighbor sum distinguishing total coloring of planar graphs

Neighbour sum distinguishing total colourings via the Combinatorial Nullstellensatz

Neighbour sum distinguishing total colourings via the Combinatorial Nullstellensatz