A connected graph is called neighbourly irregular (NI) if it contains no edge between the vertices of the same degree. In this paper we determine the upper bound for chromatic number of a neighbourly irregular graph. We also prove some results on neighbourly irregular graphs and its chromatic number.

The Fuzzy logic concept is implemented in several image processing operations such as edge detection, segmentation, object recognition, etc. In this paper, a novel Image encryption algorithm based on multiple fuzzy graph (FG) mapping technique is proposed. The Fuzzy graphs are obtained from a matrix of size n and then they are used to encrypt an image. Here fuzzy graphs with triangular and sigm...

In this paper, we study the total edge irregularity strength of some well known graphs. An edge irregular total k-labeling φ : V ∪E → {1, 2, . . . , k} of a graph G = (V,E) is a labeling of vertices and edges of G in such a way that for any different edges xy and x′y′ their weights are distinct. The total edge irregularity strength tes(G) is defined as the minimum k for which G has an edge irre...

An edge irregular total k-labeling φ : V ∪ E → {1, 2, . . . , k} of a graph G = (V,E) is a labeling of vertices and edges of G in such a way that for any different edges uv and u′v′ their weights φ(u) +φ(uv) +φ(v) and φ(u′) +φ(u′v′) +φ(v′) are distinct. The total edge irregularity strength, tes(G), is defined as the minimum k for which G has an edge irregular total k-labeling. In this paper, we...

We define binet matrices, which furnish a direct generalization of totally unimodular network matrices and arise from the node-edge incidence matrices of bidirected graphs in the same way as the network matrices do from directed graphs. We develop the necessary theory, give binet representations for interesting sets of matrices, characterize totally unimodular binet matrices and discuss the rec...

An edge-colored graph is \emph{rainbow }if no two edges of the have same color. $G^c$ called \emph{properly colored} if every adjacent receive distinct colors in $G^c$. A \emph{strongly edge-colored} a proper such that path length $3$ rainbow. We call an vertex pair-pancyclic} any vertices are contained rainbow cycle $\ell$ for each with $3 \leq \ell n$. In this paper, we show strongly order $n...

An undirected graph G is locally irregular if every two of its adjacent vertices have distinct degrees. We say that G is decomposable into k locally irregular graphs if there exists a partition E1∪E2∪ ...∪Ek of the edge set E(G) such that each Ei induces a locally irregular graph. It was recently conjectured by Baudon et al. that every undirected graph admits a decomposition into 3 locally irre...

We study the Moran process as adapted by Lieberman, Hauert and Nowak. A family of directed graphs is said to be strongly amplifying if the extinction probability tends to 0 when the Moran process is run on graphs in this family. The most-amplifying known family of directed graphs is the family of megastars of Galanis et al. We show that this family is optimal, up to logarithmic factors, since e...