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ON THE FORCING SIGNAL NUMBER OF A GRAPH

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R.Kalaivani,T.Muthu Nesa Beula
» doi: 10.48047/ecb/2023.12.10.458

Abstract

For two vertices x and y of a graph G, the set L[x,y] consist of x and y and all vertices lying on some x-y goosing of G and for a non-empty set S⊆V(G), L[S]=■(⋃@x,y∈S) L[x,y]. A set S⊆V(G) is said to be a signal set of G if L[S]=V(G). The minimum cardinality of a signal set is known as signal number and is denoted by sn(G). A subset T of a minimum signal set S is called a forcing subset for S if S is the unique minimum signal set containing T. The forcing signal number f_G s(S) of S is the minimum cardinality among the forcing subsets of S, and the forcing signal number fs(G) of G is the minimum forcing signal number among all minimum signal set of G. In this paper, the forcing signal number of several classes of graphs are determined some of its general properties also studied.

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