20.500.12556/RUL-176924 Generalized stepwise transmission irregular graphs The transmission ${\rm Tr}_G(u)$ of a vertex $u$ of a connected graph $G$ is the sum of distances from $u$ to all other vertices. $G$ is a stepwise transmission irregular (STI) graph if $|{\rm Tr}_G(u) - {\rm Tr}_G(v)|= 1$ holds for any edge $uv\in E(G)$. In this paper, generalized STI graphs are introduced as the graphs $G$ such that for some $k\ge 1$ we have $|{\rm Tr}_G(u) - {\rm Tr}_G(v)|= k$ for any edge $uv$ of $G$. It is proved that generalized STI graphs are bipartite and that as soon as the minimum degree is at least $2$, they are $2$-edge connected. Among the trees, the only generalized STI graphs are stars. The diameter of STI graphs is bounded and extremal cases discussed. The Cartesian product operation is used to obtain highly connected generalized STI graphs. Several families of generalized STI graphs are constructed. graph distance transmission of vertex stepwise transmission irregular graph Cartesian product of graphs razdalja v grafu celotna razdalja vozlišča stopenjsko iregularen graf kartezični produkt grafov true false true Angleški jezik Slovenski jezik Članek v reviji 2025-12-15 12:38:23 2025-12-15 12:38:28 2025-12-26 03:49:18 0000-00-00 00:00:00 2024 0 0 Str. 5875-5883 no. 16 Vol. 38 2024 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2024-01-01 519.17 0354-5180 10.2298/FIL2416875A 212465411 RAZ_Alizadeh_Yaser_2024.pdf RAZ_Alizadeh_Yaser_2024.pdf 1 78371CFD9EDCAD1A144A84861830DA2F a767eeaaada0c81838747a8ef02e348cc8c219201a31cc02f3c371c7b8f8a0ca 23d88f77-d9aa-11f0-9328-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=223737 https://doiserbia.nb.rs/Article.aspx?ID=0354-51802416875A 0 79237a66-d9aa-11f0-9328-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=223738 Fakulteta za matematiko in fiziko 0 0 0