TITLE

# Characterization of Line Sidigraphs

AUTHOR(S)
Sampathkumar, E.; Subramanya, M. S.; Reddy, P. Siva Kota
PUB. DATE
March 2011
SOURCE
Southeast Asian Bulletin of Mathematics;2011, Vol. 35 Issue 2, p297
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
A sigraph (sidigraph) is an ordered pair S = (G; Ïƒ) (S = (D; Ïƒ)), where G = (V, E) (D = (V, A) is a graph (digraph) called the underlying graph (underlying digraph) of S and Ïƒ : E â†’ {+, -} (&sigma: A â†’ {+, -}) is a function. The line sigraph (line sidigraph) of a sigraph (sidigraph) S = (G; Ïƒ) (S = (D; Ïƒ)) as a sigraph (sidigraph) L(S) = (L(G); Ïƒ') (L(S) = (L(D); Ïƒ')), where L(G) (L(D)) is the underlying graph (digraph) of L(S) is the line graph (digraph) of G, where for any edge (arc) Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. in L(S), Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed.. Analogous to the known result that the line sigraph of any sigraph is balanced, it is shown that line sidigraph of any sidigraph is balanced. In this paper, we define a given sigraph (sidigraph) S to be a line sigraph (line sidigraph) if there exists a sigraph (sidigraph) H such that L(H) is isomorphic to S. We then give a structural characterization of line sidigraphs. Further, in this paper, we introduce the notion switching in sidigraphs and we characterize the sidigraphs which are switching equivalent to their line sidigraphs.
ACCESSION #
64873454

## Related Articles

• A Contribution to the Second Neighborhood Problem. Ghazal, Salman // Graphs & Combinatorics;Sep2013, Vol. 29 Issue 5, p1365

Seymour's Second Neighborhood Conjecture asserts that every oriented graph (without digons) has a vertex whose first out-neighborhood is at most as large as its second out-neighborhood. It is proved for tournaments, tournaments missing a matching and tournaments missing a generalized star. We...

• Finite Tournaments with a Nonempty Diamonds' Support. Bouchaala, Houcine; Boudabbous, Youssef; Elayech, Mohamed // Graphs & Combinatorics;Nov2013, Vol. 29 Issue 6, p1653

Up to isomorphism, there are two tournaments, called diamonds, on 4 vertices and containing a unique 3-cycle. If T is a tournament containing at least a diamond, the diamonds' support of T is the intersection of all the subsets X of V ( T) such that the sub-tournament T [ X] of T, induced by X,...

• Zero Divisors Among Digraphs. Hammack, Richard; Smith, Heather // Graphs & Combinatorics;Jan2014, Vol. 30 Issue 1, p171

A digraph C is called a zero divisor if there exist non-isomorphic digraphs A and B for which $${A \times C \cong B \times C}$$ , where the operation is the direct product. In other words, C being a zero divisor means that cancellation property {A \times C \cong B \times C \Rightarrow A \cong...

• UNDERLYING GRAPHS OF 3-QUASI-TRANSITIVE DIGRAPHS AND 3-TRANSITIVE DIGRAPHS RUIXIA WANG, SHIYING WANG. RUIXIA WANG; SHIYING WANG // Discussiones Mathematicae: Graph Theory;2013, Vol. 33 Issue 2, p429

A digraph is 3-quasi-transitive (resp. 3-transitive), if for any path x0x1 x2x3 of length 3, x0 and x3 are adjacent (resp. x0 dominates x3). CÃ©sar HernÃ¡ndez-Cruz conjectured that if D is a 3-quasi-transitive digraph, then the underlying graph of D, UG(D), admits a 3-transitive orientation....

• Edge Maximal C3 and C5-Edge Disjoint Free Graphs. Bataineh, M. S. A.; Jaradat, M. M. M. // International Journal of Mathematical Combinatorics;Mar2011, Vol. 1, p82

No abstract available.

• A Note on Antipodal Signed Graphs. Reddy, P. Siva Kota; Prashanth, B.; Permi, Kavita S. // International Journal of Mathematical Combinatorics;Mar2011, Vol. 1, p107

No abstract available.

• Unique factorization of compositive hereditary graph properties. Broere, Izak; Drgas-Burchardt, Ewa // Acta Mathematica Sinica;Feb2012, Vol. 28 Issue 2, p267

A graph property is any class of graphs that is closed under isomorphisms. A graph property P is hereditary if it is closed under taking subgraphs; it is compositive if for any graphs G, G âˆˆ P there exists a graph G âˆˆ P containing both G and G as subgraphs. Let H be any given graph on...

• Note on the longest paths in { K, K + e}-free graphs. Duan, Fang; Wang, Guo // Acta Mathematica Sinica;Dec2012, Vol. 28 Issue 12, p2501

A graph G is { K, K + e}-free if G contains no induced subgraph isomorphic to K or K + e. In this paper, we show that G has a path which is either hamiltonian or of length at least 2 Î´ + 2 if G is a connected { K, K + e}-free graph on at least 7 vertices.

• The signless Laplacian spectral radius of C4-free graphs with even order. LI Guang-bin // Basic Sciences Journal of Textile Universities / Fangzhi Gaoxia;jun2013, Vol. 26 Issue 2, p171

Let G be a simple graph, the matrix Q(G)=D(G)+A(G) denotes the signless Laplacian matrix of G, where D(G) and A(G) denote the diagonal matrix of vertex degrees and the adjacency matrix of G, respectively. In this paper, we prove that if G is a C4-free graph (a graph contains no subgraphs...

Share