Generalized stepwise transmission irregular graphs

Alizadeh, Yaser (avtor), Klavžar, Sandi (avtor), Molaee, Zohre (avtor)

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.

• Jezik: Angleški jezik
• Ključne besede: graph distance, transmission of vertex, stepwise transmission irregular graph, Cartesian product of graphs
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Datum objave: 01.01.2024
• Leto izida: 2024
• Št. strani: Str. 5875-5883
• Številčenje: Vol. 38, no. 16
• PID: 20.500.12556/RUL-176924
• UDK: 519.17
• ISSN pri članku: 0354-5180
• DOI: 10.2298/FIL2416875A
• COBISS.SI-ID: 212465411
• Datum objave v RUL: 15.12.2025

Gradivo je del revije

• Naslov: Filomat
• Skrajšan naslov: Filomat
• Založnik: Department of Mathematics and Informatics, Faculty of Science and Mathematics, University of Niš
• ISSN: 0354-5180
• COBISS.SI-ID: 1024191828

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: razdalja v grafu, celotna razdalja vozlišča, stopenjsko iregularen graf, kartezični produkt grafov