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Characterization by intersection graph of some families of finite nonsimple groups

Hossein Shahsavari, Behrooz Khosravi (2021)

Czechoslovak Mathematical Journal

For a finite group G , Γ ( G ) , the intersection graph of G , is a simple graph whose vertices are all nontrivial proper subgroups of G and two distinct vertices H and K are adjacent when H K 1 . In this paper, we classify all finite nonsimple groups whose intersection graphs have a leaf and also we discuss the characterizability of them using their intersection graphs.

Characterization of 2 -minimally nonouterplanar join graphs

D. G. Akka, J. K. Bano (2001)

Mathematica Bohemica

In this paper, we present characterizations of pairs of graphs whose join graphs are 2-minimally nonouterplanar. In addition, we present a characterization of pairs of graphs whose join graphs are 2-minimally nonouterplanar in terms of forbidden subgraphs.

Characterization of block graphs with equal 2-domination number and domination number plus one

Adriana Hansberg, Lutz Volkmann (2007)

Discussiones Mathematicae Graph Theory

Let G be a simple graph, and let p be a positive integer. A subset D ⊆ V(G) is a p-dominating set of the graph G, if every vertex v ∈ V(G)-D is adjacent with at least p vertices of D. The p-domination number γₚ(G) is the minimum cardinality among the p-dominating sets of G. Note that the 1-domination number γ₁(G) is the usual domination number γ(G). If G is a nontrivial connected block graph, then we show that γ₂(G) ≥ γ(G)+1, and we characterize all connected block graphs with...

Characterization of Cubic Graphs G with ir t (G) = Ir t (G) = 2

Changiz Eslahchi, Shahab Haghi, Nader Jafari (2014)

Discussiones Mathematicae Graph Theory

A subset S of vertices in a graph G is called a total irredundant set if, for each vertex v in G, v or one of its neighbors has no neighbor in S −{v}. The total irredundance number, ir(G), is the minimum cardinality of a maximal total irredundant set of G, while the upper total irredundance number, IR(G), is the maximum cardinality of a such set. In this paper we characterize all cubic graphs G with irt(G) = IRt(G) = 2

Characterization of Line-Consistent Signed Graphs

Daniel C. Slilaty, Thomas Zaslavsky (2015)

Discussiones Mathematicae Graph Theory

The line graph of a graph with signed edges carries vertex signs. A vertex-signed graph is consistent if every circle (cycle, circuit) has positive vertex-sign product. Acharya, Acharya, and Sinha recently characterized line-consistent signed graphs, i.e., edge-signed graphs whose line graphs, with the naturally induced vertex signature, are consistent. Their proof applies Hoede’s relatively difficult characterization of consistent vertex-signed graphs. We give a simple proof that does not depend...

Characterization of n -vertex graphs with metric dimension n - 3

Mohsen Jannesari, Behnaz Omoomi (2014)

Mathematica Bohemica

For an ordered set W = { w 1 , w 2 , ... , w k } of vertices and a vertex v in a connected graph G , the ordered k -vector r ( v | W ) : = ( d ( v , w 1 ) , d ( v , w 2 ) , ... , d ( v , w k ) ) is called the metric representation of v with respect to W , where d ( x , y ) is the distance between vertices x and y . A set W is called a resolving set for G if distinct vertices of G have distinct representations with respect to W . The minimum cardinality of a resolving set for G is its metric dimension. In this paper, we characterize all graphs of order n with metric dimension n - 3 .

Characterization of power digraphs modulo n

Uzma Ahmad, Syed Husnine (2011)

Commentationes Mathematicae Universitatis Carolinae

A power digraph modulo n , denoted by G ( n , k ) , is a directed graph with Z n = { 0 , 1 , , n - 1 } as the set of vertices and E = { ( a , b ) : a k b ( mod n ) } as the edge set, where n and k are any positive integers. In this paper we find necessary and sufficient conditions on n and k such that the digraph G ( n , k ) has at least one isolated fixed point. We also establish necessary and sufficient conditions on n and k such that the digraph G ( n , k ) contains exactly two components. The primality of Fermat number is also discussed.

Characterization of semientire graphs with crossing number 2

D. G. Akka, J. K. Bano (2002)

Mathematica Bohemica

The purpose of this paper is to give characterizations of graphs whose vertex-semientire graphs and edge-semientire graphs have crossing number 2. In addition, we establish necessary and sufficient conditions in terms of forbidden subgraphs for vertex-semientire graphs and edge-semientire graphs to have crossing number 2.

Characterization Of Super-Radial Graphs

K.M. Kathiresan, G. Marimuthu, C. Parameswaran (2014)

Discussiones Mathematicae Graph Theory

In a graph G, the distance d(u, v) between a pair of vertices u and v is the length of a shortest path joining them. The eccentricity e(u) of a vertex u is the distance to a vertex farthest from u. The minimum eccentricity is called the radius, r(G), of the graph and the maximum eccentricity is called the diameter, d(G), of the graph. The super-radial graph R*(G) based on G has the vertex set as in G and two vertices u and v are adjacent in R*(G) if the distance between them in G is greater than...

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