Colouring of graphs is being used in several representations of real world systems like map colouring, traffic signalling, etc. This study introduces the edge colouring of fuzzy graphs. The chromatic index and the strong chromatic index are defined and related properties are investigated. In addition, job oriented web sites, traffic light problems have been presented and solved using the edge colouring of fuzzy graphs more effectively.

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Applications of Edge Colouring of Fuzzy Graphs

Fuzzy chromatic number of union of fuzzy graphs: An algorithm, properties and its application

An edge irregular total k-labeling on simple and undirected graph G(V,E) is a map f : V ∪ E →{1, 2,…,k} such that for any different edge xy and x′y′ their weights f(x) + f(xy) + f(y) and f(x′) + f(...

Total edge irregularity strength of ladder-related graphs

On Total Irregularity Strength of Double-Star and Related Graphs

Let $G = (V,E)$ be a simple connected graph. The eccentric-distance sum of $G$ is defined as $\xi^{ds}(G) =\ds\sum_{\{u,v\}\subseteq V(G)} [e(u)+e(v)] d(u,v)$, where $e(u)$ %\ds is the eccentricity of the vertex $u$ in $G$ and $d(u,v)$ is the distance between $u$ and $v$. In this paper, we establish formulae to calculate the eccentric-distance sum for some graphs, namely wheel, star, broom, lollipop, double star, friendship, multi-star graph and the join of $P_{n-2}$ and $P_2$.

The eccentric-distance sum of some graphs

Let G = (V, E) be a simple, connected and undirected graph with non empty vertex set V and edge set E. An edge irregular total k-labeling ${f: V(G)\cup E(G) \to \{ 1,2, \ldots, k \}}$ is a labeling of vertices and edges of G in such a way that for any different edges xy and x′y′ their weights f(x) + f(xy) + f(y) and f(x′) + f(x′y′) + f(y′) are distinct. A total edge irregularity strength of graph G, denoted by tes(G), is defined as the minimum k for which G has an edge irregular total k-labeling. In this paper, we determine the exact value of the total edge irregularity strength of the generalized web graph W(n, m) and two families of related graphs.

On Total Edge Irregularity Strength of Generalized Web Graphs and Related Graphs

Edge Irregular Reflexive Labeling on Corona of Path and Other Graphs

Matlab algorithms for traffic light assignment using fuzzy graph, fuzzy chromatic number, and fuzzy inference system.

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