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[PDF] Top 20 On the rainbow neighbourhood number of set-graphs

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On the rainbow neighbourhood number of set-graphs

On the rainbow neighbourhood number of set-graphs

... colouring set is complied with. Also, since each set X i is an independent set of vertices the colouring is a proper ...the rainbow neighbourhood convention in that, after a maximum ... See full document

9

An Optimal Algorithm to Find a Minimum 2-neighbourhood Covering Set on Cactus Graphs

An Optimal Algorithm to Find a Minimum 2-neighbourhood Covering Set on Cactus Graphs

... where leaf nodes contain 4 m + 1 and 4 m + 2 vertices. Sometimes, these contribute m vertices in X instead of m + 1 vertices as in Lemma 4. Similarly, for the tree block the paths containing 4 m + 1 and 4 m + 2 edges ... See full document

15

Rainbow numbers for small cycles

Rainbow numbers for small cycles

... the class of all the maximal outerplanar graphs of order n. For two disjoint subsets R, T ⊆ V (G), denote by E G [R, T ] the set of all the edges between R and T in G. We use G[R] to denote the subgraph ... See full document

7

An updated survey on rainbow connections of graphs - a dynamic survey

An updated survey on rainbow connections of graphs - a dynamic survey

... the rainbow connection number which is defined on vertex-colored ...is rainbow vertex-connected if any two vertices are connected by a path whose internal vertices have distinct ...is rainbow ... See full document

67

Some Bounds of Rainbow Edge Domination in Graphs

Some Bounds of Rainbow Edge Domination in Graphs

... dominating set. The edge domination number is the cardinality of minimal edge dominating ...the set of all edges adjacent to in G, further N [ ]=N( )∪{ is the closed neighborhood of “ in ... See full document

11

Rainbow number of matchings in Halin graphs

Rainbow number of matchings in Halin graphs

... Halin graphs as a class of minimally 3-vertex-connected graphs: for every edge in the graph, the removal of that edge reduces the connectivity of the ...These graphs gained in significance with the ... See full document

13

Colored complete hypergraphs containing no rainbow Berge triangles

Colored complete hypergraphs containing no rainbow Berge triangles

... In order to extend these results to hypergraphs that are not 3-uniform, we first define what it means to be “complete”. A hypergraph H is called 3-complete if, for each set of 3 vertices, there is a distinct ... See full document

11

Geometric Number of Planar Graphs

Geometric Number of Planar Graphs

... the set of all points in the plane that can be reached from x by traversing along a curve that does not have a vertex of the graph or a point of an edge as an intermediate point, is the region of the graph that ... See full document

7

Note on Rainbow Connection in Oriented Graphs with Diameter 2

Note on Rainbow Connection in Oriented Graphs with Diameter 2

... called rainbow if no two edges have the same color within the ...directed rainbow path between every pair of vertices in a graph, then the coloring is called rainbow ...smallest number of ... See full document

7

On Steiner Domination Number of Graphs

On Steiner Domination Number of Graphs

... Suppose W = {x, y} is a Steiner dominating set ofG * . Therefore, x and y are notadjacent in G * . Then, W is any one of the following three sets, they are {u, v},{v,w} and {w, x}. In all the three cases, there is ... See full document

5

Neighbourhood Edge Product Cordial And Total Neighbourhood Edge Product Cordial Labeling Of Graphs

Neighbourhood Edge Product Cordial And Total Neighbourhood Edge Product Cordial Labeling Of Graphs

... concepts neighbourhood edge product cordial labeling and total neighbourhood edge product cordial labeling of graph and present the neighbourhood edge product cordial labeling of Paths, kG, G 1 ∪G 2 ... See full document

8

On graphs with representation number 3

On graphs with representation number 3

... copies of x. By symmetry, without loss of generality we can assume that x = 1. Further, using Propositions 2 and 5, we only need to consider two cases (the second one is unnecessary in the case of n = 4 because of ... See full document

14

A NOTE ON CERTAIN TOPOLOGICAL INDICES OF THE DERIVED GRAPHS OF SUBDIVISION GRAPHS

A NOTE ON CERTAIN TOPOLOGICAL INDICES OF THE DERIVED GRAPHS OF SUBDIVISION GRAPHS

... Abstract. In this note, we correct some errors in S. M. Hosamani et al. [TWMS J. App. Eng. Math., 6(2), (2016) pp. 324–332]. The derived graph [G] † of a graph G is the graph having the same vertex set as G, with ... See full document

12

On the edge set of graphs of lattice paths

On the edge set of graphs of lattice paths

... Thus, we have accounted for every path in L(m, 2) in one of the cases above, and for each path, we have counted all its equivalent paths. However, each pair of paths has been counted exactly twice, one time for each path ... See full document

9

Strong LICT Domination in Graphs

Strong LICT Domination in Graphs

... A set  ( ) is a dominating set of , if every vertex in − is adjacent to some vertex in ...a set is called the domination number of and is denoted by ( ...dominating set  ( ) is a ... See full document

10

Set-Valuations of Graphs and their Applications: A Survey

Set-Valuations of Graphs and their Applications: A Survey

... the set f M ' ( u ) = { d ( u , v ) : v ∈ M }, where d(x, y) denotes the usual distance between the vertices x and y in G, called the M-distance pattern of ...injective set-valued function when restricted ... See full document

35

Some Classes of Set Graceful Graphs

Some Classes of Set Graceful Graphs

... /E(G)/ = 2n+1 − 1. Define Xn = {1, 2, 3, ....n} . Define the labeling f: V (G) → 2Xn+1 as follows.Label u byXn+1 and vi by subsets of Xn , for each i = 1, 2, ....2n in such a way that T is Set graceful.Then the ... See full document

7

Trivial Fuzzy Topology of the Set of Fuzzy Graphs

Trivial Fuzzy Topology of the Set of Fuzzy Graphs

... fuzzy set which is characterized by a membership function that assigns a grade of membership ranging from 0 to 1to each of its ...the set of fuzzy ...the set of fuzzy ...fuzzy graphs are ... See full document

11

Cartesian product and Neighbourhood Polynomial of a Graph

Cartesian product and Neighbourhood Polynomial of a Graph

... 1.2 Neighbourhood complex and polynomial- A complex on a finite set 𝒳 is a collection 𝒞 of subsets of 𝒳, closed under certain predefined ...Each set in 𝒞 is called the face of the complex. In the ... See full document

5

On the Non Common Neighbourhood Energy of Graphs

On the Non Common Neighbourhood Energy of Graphs

... Abstract In this paper, we introduce a new type of graph energy called the non-common-neighborhood energy ENCN G , NCN-energy for some standard graphs is obtained and an upper bound fo[r] ... See full document

6

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