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Extremal results on stepwise transmission irregular graphs
Alizadeh, Yaser ; Klavžar, Sandi
Celotna razdalja ▫${\rm Tr}_G(v)$▫ vozlišča ▫$v$▫ povezanega grafa ▫$G$▫ je vsota razdalj med ▫$v$▫ in vsemi drugimi vozlišči v ▫$G$▫. ▫$G$▫ je stopenjsko iregularen graf za celotno razdaljo (STI), ...če ▫$|{\rm Tr}_G(u) - {\rm Tr}_G(v)| =1$▫ velja za vsako povezavo ▫$uv \in E(G)$▫. V tem članku so dokazani ekstremni rezultati za grafe STI glede na število povezav in različne metrične lastnosti. V vseh primerih se pojavljata dve ekstremni družini, uravnoteženi polni dvodelni grafi lihega reda in tako imenovani lihi klobučni cikli.
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