# PLANARITY OF ECCENTRIC DIGRAPH OF GRAPHS

## Related Articles

- THE ECCENTRIC DIGRAPH OF CORONA OF CYCLE WITH ANY GRAPH H. Tri Atmojo Kusmayadi; Yemi Kuswardi; Budi Usodo; Nugroho Arif Sudibyo // Far East Journal of Mathematical Sciences;Jun2015, Vol. 97 Issue 4, p407
Let G be a graph with a set of vertices V (G) and a set of edges E(G). The distance from vertex u to vertex v in G is the length of the shortest path from vertex u to v. The eccentricity e(u) of a vertex u is the maximum distance of u to any other vertices of G. A vertex v is an eccentric vertex...

- THE ECCENTRIC DIGRAPH OF A GENERALIZED FLOWER GRAPH. Kusmayadi, Tri Atmojo; Kuntari, Sri; Sudibyo, Nugroho Arif // Far East Journal of Mathematical Sciences;Jun2016, Vol. 99 Issue 11, p1771
Let G be a graph with a set of vertices V(G) and a set of edges E(G). The distance from vertex u to vertex v in G is the length of the shortest path from vertex u to v. The eccentricity e(u) of a vertex u is the maximum distance of u to any other vertices of G. A vertex v is an eccentric vertex...

- A Characterization of Directed Paths. S., Ramya.; M., Nagesh. H. // International Journal of Mathematical Combinatorics;Jun2015, Vol. 2, p144
In this note, the non-trivial connected digraphs D with vertex set V (D) = {v1, v2, ..., vn} satisfying ... are characterized, where d- (vi) and d+ (vi) be the in-degree and out-degree of vertices of D, respectively.

- An Infinite Family of Planar Hypohamiltonian Oriented Graphs. Aardt, Susan; Burger, Alewyn; Frick, Marietjie // Graphs & Combinatorics;Jul2013, Vol. 29 Issue 4, p729
Carsten Thomassen asked in 1976 whether there exists a planar hypohamiltonian oriented graph. We answer his question by presenting an infinite family of planar hypohamiltonian oriented graphs, the smallest of which has order 9. A computer search showed that 9 is the smallest possible order of a...

- A Planar 3-Convex Set is Indeed a Union of Six Convex Sets. Nitzan, Noa; Perles, Micha // Discrete & Computational Geometry;Apr2013, Vol. 49 Issue 3, p454
Suppose S is a planar set. Two points $$a,b$$ in S see each other via S if $$[a,b]$$ is included in S . F. Valentine proved in 1957 that if S is closed, and if for every three points of S, at least two see each other via S, then S is a union of three convex sets. The pentagonal star shows that...

- The Scrambling Index of a Class of Two-colored Hamiltonian Digraphs. Mardiningsih; Pasaribu, Merryanty L. // AIP Conference Proceedings;2016, Vol. 1775 Issue 1, p1
The scrambling index of a two-colored digraph is the least positive integer h + â„“ over all pairs of nonnegative integers (h, â„“) such that for each pair of vertices u and v there is a vertex w with the property that there exist a walk from u to w and a walk from v to w that consist...

- Semitotal Domination in Claw-Free Cubic Graphs. Henning, Michael; Marcon, Alister // Annals of Combinatorics;Dec2016, Vol. 20 Issue 4, p799
In this paper, we continue the study of semitotal domination in graphs in [Discrete Math. 324, 13-18 (2014)]. A set $${S}$$ of vertices in $${G}$$ is a semitotal dominating set of $${G}$$ if it is a dominating set of $${G}$$ and every vertex in $${S}$$ is within distance 2 of another vertex of...

- Total coloring of planar graphs without chordal 7-cycles. Cai, Hua // Acta Mathematica Sinica;Dec2015, Vol. 31 Issue 12, p1951
A k-total-coloring of a graph G is a coloring of vertices and edges of G using k colors such that no two adjacent or incident elements receive the same color. In this paper, it is proved that if G is a planar graph with Î”( G) â‰¥ 7 and without chordal 7-cycles, then G has a (Î”(...

- UNICYCLIC GRAPHS WITH STRONG EQUALITY BETWEEN THE 2-RAINBOW DOMINATION AND INDEPENDENT 2-RAINBOW DOMINATION NUMBERS. AMJADI, J.; CHELLALI, M.; FALAHAT, M.; SHEIKHOLESLAMI, S. M. // Transactions on Combinatorics;Jun2015, Vol. 4 Issue 2, p1
A 2-rainbow dominating function (2RDF) on a graph G = (V, E) is a function Âƒ from the vertex set V to the set of all subsets of the set {1, 2} such that for any vertex v âˆˆ V with Âƒ(v) = Ã¸ the condition âˆªuâˆˆN(v) Âƒ(u) = {1, 2} is fulfilled. A 2RDF Âƒ is independent...