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AIP Conference Proceedings, ISSN 0094-243X, 06/2019, Volume 2112, Issue 1
A dominating set D of a graph G = G(V, E) G = G(V, E) is called metro dominating set of D. If for every pair vertices u, v there is a vertex w in D, such that... 
Apexes
Journal Article
IEEE Transactions on Dependable and Secure Computing, ISSN 1545-5971, 05/2018, Volume 15, Issue 3, pp. 542 - 548
A network's diagnosability is the maximum number of faulty vertices the network can discriminate solely by performing mutual tests among the vertices. It is an... 
Apexes
Journal Article
AIP Conference Proceedings, ISSN 0094-243X, 06/2019, Volume 2112, Issue 1
Let S ⊆ V(G). Then S is said to resolve the whole graph G if every vertex in V(G) is uniquely determined by its distance-vector to all vertices in the set S.... 
Apexes | Graphs
Journal Article
AIP Conference Proceedings, ISSN 0094-243X, 06/2019, Volume 2112, Issue 1
A vertex v ∈ V(G) that lies at the same distance from at least two distinct vertices u and w is said to be a distance similar vertex with respect to u and w. A... 
Apexes | Graphs
Journal Article
AIP Conference Proceedings, ISSN 0094-243X, 06/2019, Volume 2112, Issue 1
A dominating set D of any graph G (simple and connected) is a set in which each vertex in V-D is adjacent to atleast one vertex in D. The number of vertices in... 
Apexes | Graphs
Journal Article
AIP Conference Proceedings, ISSN 0094-243X, 06/2019, Volume 2112, Issue 1
In this paper, the Mean D-Distance, concept introduced by considering the degrees of various vertices presented in the path for some standard Radial and Detour... 
Apexes | Graphs
Journal Article
Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 04/2019, pp. 1 - 23
In this paper, we study the widely considered endomorphisms and weak endomorphisms of a finite undirected path from monoid generators perspective. Our main aim... 
Apexes | Monoids
Journal Article
Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 01/2019, pp. 1 - 10
Let G=(V,E) be a graph with no isolated vertex. A subset S⊆V(G) is a total dominating set of graph G if every vertex in V(G) is adjacent to at least one vertex... 
Apexes | Graphs
Journal Article
The Mathematical Gazette, ISSN 0025-5572, 07/2019, Volume 103, Issue 557, pp. 222 - 232
In the present paper, we show that the point of intersection of the bimedians of a cyclic quadrilateral belongs to the nine-point circle (Euler’s circle) of... 
Apexes | Quadrilaterals
Journal Article
TWMS Journal of Applied and Engineering Mathematics, 01/2019, Volume 9, Issue 3, p. 581
Two graphs of same order are said to be distance equienergetic if their distance energies are same. In this paper, we ?rst give a partial insight on the... 
Apexes | Graphs
Journal Article
AIP Conference Proceedings, ISSN 0094-243X, 08/2019, Volume 2138, Issue 1
The initial idea of Half Butterfly Method (HBM) has been introduced in 2015 to solve the geometric representation of distinct Hamiltonian circuit with... 
Apexes | Circuits | Butterflies
Journal Article
AIP Conference Proceedings, ISSN 0094-243X, 06/2019, Volume 2112, Issue 1
A dominating set whose deletion disconnects the graph is called a split dominating set S. The number of elements in a minimum S set is called the split... 
Deletion | Apexes | Graphs
Journal Article
AIP Conference Proceedings, ISSN 0094-243X, 06/2019, Volume 2112, Issue 1
For a finite simple graph X, the 2-distance graph T2(X) of X is the graph having V(X) as its vertex set and two vertices u and v in T2(X) are adjacent if and... 
Apexes | Graphs | Graph theory
Journal Article
Theory of Computing Systems, ISSN 1432-4350, 07/2019, pp. 1 - 12
A vertex set C of a graph G = (V, E) is a 3-path vertex cover if every path on 3 vertices has at least one vertex in C. This paper studies the online version... 
Natural algorithms | Apexes
Journal Article
International Journal of Algebra and Computation, ISSN 0218-1967, 09/2019, Volume 29, Issue 6, pp. 1063 - 1082
Let Λ be a finite dimensional string algebra over a field with the quiver Q such that the underlying graph of Q is a tree, and let | Det ( Λ ) | be the number... 
Algebra | Apexes | Strings
Journal Article
Journal of Mathematical Sciences, ISSN 1072-3374, 08/2019, Volume 240, Issue 5, pp. 539 - 550
We study the refined Kingman graph 𝔻, first introduced by Gnedin, whose vertices are indexed by the set of compositions of positive integers and... 
Integers | Apexes | Graph theory
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 05/2019, Volume 261, p. 119
We give an O(n4) algorithm to find a minimum clique cover of a (bull, C4)-free graph, or equivalently, a minimum colouring of a (bull, 2K2)-free graph, where n... 
Coloring | Algorithms | Apexes | Graph theory
Journal Article
Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 07/2019, pp. 1 - 11
A recent variation of the classical geodetic problem, the strong geodetic problem, is defined as follows. If G is a graph, then sg(G) is the cardinality of a... 
Apexes | Graphs | Geodesy
Journal Article
Acta Mathematicae Applicatae Sinica, English Series, ISSN 0168-9673, 04/2019, Volume 35, Issue 2, pp. 444 - 451
A graph is called traceable if it contains a Hamilton path, i.e., a path passing through all the vertices. Let G be a graph on n vertices. G is called... 
Apexes | Graph theory
Journal Article
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