TITLE

# SOME RESULTS ON SEMI-TOTAL SIGNED GRAPHS

AUTHOR(S)
SINHA, DEEPA; GARG, PRAVIN
PUB. DATE
November 2011
SOURCE
Discussiones Mathematicae: Graph Theory;2011, Vol. 31 Issue 4, p625
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
A signed graph (or sigraph in short) is an ordered pair S = (SuÎ´), where Su is a graph G = (V,E), called the underlying graph of S and Î´ : E â†’ {+,-} is a function from the edge set E of Suinto the set {+,-}, called the signature of S. The x-line sigraph of S denoted by L x (S) is a sigraph defined on the line graph L(Su) of the graph Suby assigning to each edge of L(Su), the product of signs of the adjacent edge âˆˆ e and f in S. In this paper, first we define semi-total line sigraph and semi-total point sigraph of a given sigraph and then characterize balance and consistency of semi-total line sigraph and semi-total point sigraph.
ACCESSION #
66787065

## Related Articles

• 3-TRANSITIVE DIGRAPHS. Hernández-Cruz, César // Discussiones Mathematicae: Graph Theory;2012, Vol. 32 Issue 3, p205

Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. A digraph D is 3-transitive if the existence of the directed path (u; v;w; x) of length 3 in D implies the existence of the arc (u, x) âˆˆ A(D). In this article strong 3-transitive digraphs are...

• Majority Domatic Number - I. Manora, J. Joseline; Swaminathan, V. // Global Journal of Pure & Applied Mathematics;2010, Vol. 6 Issue 3, p275

In any democratic set up, the party which has majority of seats is given the opportunity to rule the state. To model such instances, the concept majority domination is introduced. This chapter deals with partitioning the vertex set into as many disjoint subsets, each being a majority dominating...

• THE i-CHORDS OF CYCLES AND PATHS. MCKEE, TERRY A. // Discussiones Mathematicae: Graph Theory;2012, Vol. 32 Issue 4, p607

An i-chord of a cycle or path is an edge whose endpoints are a distance i â‰¥ 2 apart along the cycle or path. Motivated by many standard graph classes being describable by the existence of chords, we investigate what happens when i-chords are required for specific values of i. Results...

• Graph Equation for Line Graphs and m-Step Graphs. Kim, Seog-Jin; Kim, Suh-Ryung; Lee, Jung; Park, Won; Sano, Yoshio // Graphs & Combinatorics;Nov2012, Vol. 28 Issue 6, p831

Given a graph G, the m-step graph of G, denoted by S( G), has the same vertex set as G and an edge between two distinct vertices u and v if there is a walk of length m from u to v. The line graph of G, denoted by L( G), is a graph such that the vertex set of L( G) is the edge set of G and two...

• An Algorithm to Detect Cycle in an Undirected Graph. Kumar, Anand; Jani, N. N. // International Journal of Computational Intelligence Research;2010, Vol. 6 Issue 2, p305

This paper presents a novel algorithm to detect cycles in a graph. The graph may be of any type. Cycles are available in a graph and in much real life application; it is required to know the existence of cycles in a graph. This algorithm is developed in the context of network design problem but...

• ON MONOCHROMATIC PATHS AND BICOLORED SUBDIGRAPHS IN ARC-COLORED TOURNAMENTS. DELGADO-ESCALANTE, PIETRA; GALEANA-SANCHEZ, HORTENSIA // Discussiones Mathematicae: Graph Theory;2011, Vol. 31 Issue 4, p791

Consider an arc-colored digraph. A set of vertices N is a kernel by monochromatic paths if all pairs of distinct vertices of N have no monochromatic directed path between them and if for every vertex v not in N there exists n âˆˆ N such that there is a monochromatic directed path from v to n....

• ON THE TOTAL RESTRAINED DOMINATION NUMBER OF DIRECT PRODUCTS OF GRAPHS. WAI CHEE SHIU; HONG-YU CHEN; XUE-GANG CHEN; PAK KIU SUN // Discussiones Mathematicae: Graph Theory;2012, Vol. 32 Issue 4, p629

Let G = (V,E) be a graph. A total restrained dominating set is a set S âŠ† V where every vertex in V \ S is adjacent to a vertex in S as well as to another vertex in V \ S, and every vertex in S is adjacent to another vertext in S. The total restrained domination number of G, denoted by...

• DOUBLE DOMINATION CRITICAL AND STABLE GRAPHS UPON VERTEX REMOVAL. KHELIFI, SOUFIANE; CHELLALI, MUSTAPHA // Discussiones Mathematicae: Graph Theory;2012, Vol. 32 Issue 4, p643

In a graph a vertex is said to dominate itself and all its neighbors. A double dominating set of a graph G is a subset of vertices that dominates every vertex of G at least twice. The double domination number of G, denoted Î³x2(G), is the minimum cardinality among all double dominating sets of...

• FINITE TOPOLOGIES AND DIGRAPHS. MARIJUÁN, CARLOS // Proyecciones - Journal of Mathematics;2010, Vol. 29 Issue 3, p291

In this paper we study the relation between finite topologies and digraphs. We associate a digraph to a topology by means of the "specialization" relation between points in the topology. Reciprocally, we associate a topology to each digraph, taking the sets of vertices adjacent (in the digraph)...

Share