# SOME RESULTS ON SEMI-TOTAL SIGNED GRAPHS

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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...

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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...

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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...

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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....

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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...

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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...

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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)...