Cordial Graphs Research Articles

Multiply Divisor Cordial Labeling

A Graph G* having multiply divisor cordial labeling with node set V* is a bijective. t on V * to {1,2,…,V * } such that an edge ab is allocate the label 1 if 2 divides (t (a) t (b)) and 0 otherwise, then the number of edges having label 0 and the number of edges having label 1 differ by maximum 1. A graph having multiply divisor cordial labeling is said to be multiply divisor cordial graph. In this paper, we prove that cycle, cycle having 1 chord, cycle having 2 chords, cycle having triangle, path, jellyfish, coconut tree, star and bistar graph are multiply divisor cordial graphs.

Extended results on sum divisor cordial labeling

A sum divisor cordial labeling of a graph G with vertex set V (G) is a bijection f : V (G) → {1, 2, ..., |V (G)|} such that an edge uv assigned the label 1 if 2 divides f(u)+f(v) and 0 otherwise. Further the number of edges labeled with 0 and the the number of edges labeled with 1 differ by atmost 1. A graph with sum divisor cordial labeling is called a sum divisor cordial graph. In this paper we prove that the graphs Pn + Pn (n is odd), Pn@K1,m, Cn@K1,m (n is odd), Wn ∗ K1,m (n is even), , are sum divisor cordial graphs.

Further results on 3-product cordial labeling

A mapping f : V (G) → {0, 1, 2} is called 3-product cordial labeling if |vf(i) − vf(j)| ≤ 1 and |ef(i) − ef(j)| ≤ 1 for any i, j ∈ {0, 1, 2}, where vf(i) denotes the number of vertices labeled with i, ef(i) denotes the number of edges xy with f(x)f(y) ≡ i(mod 3). A graph with 3-product cordial labeing is called 3-product cordial graph. In this paper we establish that switching of an apex vertex in closed helm, double fan, book graph K1,n × K2 and permutation graph P (K2 + mK1, I) are 3-product cordial graphs.

On edge product cordial graphs

An edge product cordial labeling is a variant of the well-known cordial labeling. In this paper we characterize graphs admitting an edge product cordial labeling. Using this characterization we investigate the edge product cordiality of broad classes of graphs, namely, dense graphs, dense bipartite graphs, connected regular graphs, unions of some graphs, direct products of some bipartite graphs, joins of some graphs, maximal \(k\)-degenerate and related graphs, product cordial graphs.

Duplicating a Vertex with an Edge in Divided Square Difference Cordial Graphs

In this present work, we discuss divided square difference (DSD) cordial labeling in the context of duplicating a vertex with an edge in DSD cordial graphs such as path graph, cycle graph, star graph, wheel graph, helm graph, crown graph, comb graph and snake graph.

Path Related Balanced Divided Square Difference Cordial Graphs

Path Related Balanced Divided Square Difference Cordial Graphs

Cycle Related Balanced Divided Square Difference Cordial Graphs

Cycle Related Balanced Divided Square Difference Cordial Graphs

SD and k-SD Prime Cordial graphs

In this paper, we investigate the SD-Prime cordial labeling of Pln graph and k-SD-Prime cordial labeling of (PnOK1) ∪ K1,n,n and Pn∪K1,n,n.

3-Total Sum Cordial Labeling on Some New Graphs

Let \(G=(V,E)\) be a graph with vertex set \(V\) and edge set \(E\). Consider a vertex labeling \(f:V(G)\to \{0,1,2\}\) such that each edge \(uv\) assign the label \((f(u)+f(v)) (\{{\rm mod}\ 3)\). The map \(f\) is called a 3-total sum cordial labeling if \(|f(i)-f(j)|\le 1\), for \(i,j \in \{0,1,2\}\) where \(f(x)\) denotes the total number of vertices and edges labeled with \(x=\{0,1,2\}\). Any graph which satisfied 3-total sum cordial labeling is called a 3-total sum cordial graph. Here we prove some graphs like wheel, globe and a graph obtained by switching and duplication of arbitrary vertex of a cycle are 3-total sum cordial graphs.

Some New Results on Sum Divisor Cordial Graphs

Some New Results on Sum Divisor Cordial Graphs

Prime Cordial Labeling

We show that some special families of graphs have prime cordial labeling. We prove that If G is not a prime cordial graph of order m then G∪K_(1,n)is a prime cordial graph if E(G)= n-1,n or n+1 , and we prove that S^' (K_(2,n)), Jelly fish graph , Jewel graph, the graph obtained by duplicating a vertex v_k in the rim of the helm H_nand the graph obtained by fusing the vertex u_1 with u_3in a Helm graphH_n are prime cordial graphs.

English

English

Sum divisor cordial labeling for star and ladder related graphs

A sum divisor cordial labeling of a graph G with vertex set V is a bijection f from V to {1, 2, . . . , |V(G)|} such that an edge uv is assigned the label 1 if 2 divides f (u) + f (v) and 0 otherwise; and the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. A graph with a sum divisor cordial labeling is called a sum divisor cordial graph. In this paper, we prove that D2(K1,n), S' (K1,n), D2(Bn,n), DS(Bn,n), S' (Bn,n), S(Bn,n), , S(Ln), Ln O K1, SLn, TLn, TLn O Ki and CHn are sum divisor cordial graphs.

English

English

Sum divisor cordial graphs

A sum divisor cordial labeling of a graph G with vertex set V is a bijection f from V (G) to {1, 2, ..., |V (G)|} such that an edge uv is assigned the label 1 if 2 divides f (u) + f (v) and 0 otherwise, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. A graph with a sum divisor cordial labeling is called a sum divisor cordial graph. In this paper, we prove that path, comb, star, complete bipartite, K2+ mK1, bistar, jewel, crown, flower, gear, subdivision of the star, K1,3* K1,n and square graph of Bn,n are sum divisor cordial graphs.

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.

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

Product Cordial Graph in the Context of Some Graph Operations on Gear Graph

A graph is said to be a product cordial graph if there exists a function with each edge assign the label , such that the number of vertices with label 0 and the number of vertices with label 1 differ atmost by 1, and the number of edges with label 0 and the number of edges with label 1 differ by atmost 1. We discuss the product cordial labeling of the graphs obtained by duplication of some graph elements of gear graph. Also, we derive some product cordial graphs obtained by vertex switching operation on gear graph.

Some Edge Product Cordial Graphs in the Context of Duplication of Some Graph Elements

For a graph, a function is called an edge product cordial labeling of G, if the induced vertex labeling function is defined by the product of the labels of the incident edges as such that the number of edges with label 1 and the number of edges with label 0 differ by at most 1 and the number of vertices with label 1 and the number of vertices with label 0 differ by at most 1. In this paper, we show that the graphs obtained by duplication of a vertex, duplication of a vertex by an edge or duplication of an edge by a vertex in a crown graph are edge product cordial. Moreover, we show that the graph obtained by duplication of each of the vertices of degree three by an edge in a gear graph is edge product cordial. We also show that the graph obtained by duplication of each of the pendent vertices by a new vertex in a helm graph is edge product cordial.

Some results and examples on difference cordial graphs

In this paper we introduce some results on difference cordial graphs and describe the difference cordial labeling for some families of graphs.