On Characterization of Balance and Consistency Preserving d-Antipodal Signed Graphs
نویسندگان
چکیده
A signed graph is an ordered pair Σ=(G,σ), where G a and σ:E(G)⟶{+1,−1} mapping. For e∈E(G), σ(e) called the sign of e for any sub-graph H G, σ(H)=∏e∈E(H)σ(e) H. having each cycle +1 balanced. Two vertices in are antipodal if dG(u,v)=diam(G). The A(G) with vertex set that same as two u,v adjacent antipodal. By d-antipodal GdA we refer to union A(G). Given ΣdA=(GdA,σd) σd defined follows: σd(e)=σ(e)ife∈E(G)andotherwise,σd(e)=∏P∈Peσ(P), Pe collection all diametric paths Σ connecting end edge ΣdA. In this article, balance property canonical consistency graphs Smith (connected highest eigenvalue 2) studied.
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ژورنال
عنوان ژورنال: Mathematics
سال: 2023
ISSN: ['2227-7390']
DOI: https://doi.org/10.3390/math11132982