[PDF] Top 20 Edge Chromatic 5-Critical Graphs

... An edge-colouring of a graph is an assignment of colours to its edges so that no two adjacent edges are assigned the same ...The chromatic index of a graph G, denoted by χ ′ (G), is the minimum number of ... See full document

... on edge coloring was written by Tait in 1880 and he proved that, if the four color conjecture is true then the edges of every 3-connected planar graph can be properly colored using only three ...cubic ... See full document

... a critical graph with maximum degree ...an edge uv such that ∆(G) − deg(v) + 2 is more than the number of vertices with maximum degree in G, then by the above argument and Vizing’s Theorem, we have χ ′ (G) ... See full document

... split graphs. It follows that a connected graph is 1-critical in respect of its CHP and CHI in that the addition (or deletion) of a vertex (or vertices) or the addition (or deletion) of an edge (or ... See full document

... resolving edge coloring (or independent resolving decomposition) of G in ...resolving edge coloring of G is an edge coloring that distinguishes all edges of G in terms of their distances from the ... See full document

... or edge coloring) problems are important to model various real time applications [6] such as traffic planning, VLSI design, circuit routing, psychology, scheduling, transportation, ...An edge coloring of a ... See full document

... the chromatic number of G and is denoted by ( ...4, 5, 6] and a detailed study of this parameter and critical graphs with respect to it were studied by Suresh Kumar in his doctoral ... See full document

... (how critical) the parameters are in respect of edge deletion, edge addition, vertex deletion or vertex insertion and ...after chromatic completion of a graph G which has been assigned a ... See full document

... needed in a total dominator coloring of G .This concept was introduced by A.Vijiyalekshmi in[2]. This notion is also referred as a smarandachely k-dominator coloring of G (k≥1) and was introduced by A.Vijiyalekshmi ... See full document

... fuzzy graphs, which are analogous to the concept corona product in crisp graph ...an edge in fuzzy graph which are obtained from two fuzzy graphs using corona product ...an edge in the corona ... See full document

... Fuzzy graph coloring is one of the most important problems of fuzzy graph theory. It uses in combinatorial optimization like traffic light control, exam-scheduling, register allocation etc. [12]. The first definition of ... See full document

... game chromatic number are χ ( ) G ≤ χ g ( ) G ≤ ∆ ( ) G + 1 , [1]. In [5], Faigle et ...game chromatic number of tree graphs and proved that χ g ( ) T ≤ 4 ...game chromatic number of ... See full document

... Sequential join is a graph operation that is introduced by Harary 1181. Graphs obtained by using this operation, represent a communication network construction [2]. Consider for three or more disjoint ... See full document

... the chromatic polynomial of ...of chromatic polynomials from maps to ...on chromatic polynomials of graphs and others obtained results on the roots of chromatic polynomials of planar ... See full document

... dominator chromatic number of middle and total graphs and compared these parameters with dominator chromatic number of the corresponding graph ...of graphs for which this chromatic ... See full document

... The neighborhood graph N(G) of a graph G = (V, E) is the graph with the vertex set V∪S where S is the set of all open neighborhood sets of vertices of G and with two vertices u, v ∈ V ∪ S adjacent if u ∈ V and v is an ... See full document

... thorny graphs in crisp graph theory is defined. The degree of an edge in thorny fuzzy graphs is ...an edge in fuzzy graph formed by this operation in terms of the degree of edges in the given ... See full document

... Algebraic methods for chromatic polynomials Philipp Augustin Reinfeld London School of Economies and Politicai Science Ph D 2 Abstract The chromatic polynomials of certain families of graphs can be ca[.] ... See full document

... of graphs for which the upper bound is ...of graphs for which the upper bound is ...and chromatic number and characterize the corresponding extremal fuzzy ... See full document

... condition ||𝑉 | − |𝑉 || ≤ 1 holds for every pair of (𝑖, 𝑗), then G is said to be equitably k-colorable. The smallest integer k for which G is equitably k-colorable is known as Equitable chromatic number of G and ... See full document