# THE i-CHORDS OF CYCLES AND PATHS

## Related Articles

- 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...

- 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...

- 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...

- 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...

- SOME RESULTS ON SEMI-TOTAL SIGNED GRAPHS. SINHA, DEEPA; GARG, PRAVIN // Discussiones Mathematicae: Graph Theory;2011, Vol. 31 Issue 4, p625
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...

- 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...

- TREES WITH EQUAL 2-DOMINATION AND 2-INDEPENDENCE NUMBERS. Chellali, Mustapha; Meddah, Nacéra // Discussiones Mathematicae: Graph Theory;2012, Vol. 32 Issue 3, p263
Let G = (V,E) be a graph. A subset S of V is a 2-dominating set if every vertex of V - S is dominated at least 2 times, and S is a 2-independent set of G if every vertex of S has at most one neighbor in S. The minimum cardinality of a 2-dominating set a of G is the 2-domination number Î³2(G)...

- A Variation of Decomposition Under a Length Constraint. Hamid, Ismail Sahul; Joseph, Mayamma // International Journal of Mathematical Combinatorics;Dec2011, Vol. 4, p35
Let í’«1 and í’«2 be graphical properties. A Smarandachely (í’«1, í’«2)- decomposition of a graph G is a decomposition of G into subgraphs G1,G2, â‹¯ , Gl âˆˆ í’« such that Gi âˆˆ í’«1 or Gi âˆ‰ í’«2 for integers 1 â‰¤ i â‰¤ l. Particularly, if...