Geodesic
Extremal results on stepwise transmission irregular graphs
Filomat, Tome 37 (2023) no. 4, p. 1271

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DOI

The transmission Tr G (v) of a vertex v of a connected graph G is the sum of distances between v and all other vertices in G. G is a stepwise transmission irregular (STI) graph if |Tr G (u) − Tr G (v)| = 1 holds for each edge uv ∈ E(G). In this paper, extremal results on STI graphs with respect to the size and different metric properties are proved. Two extremal families appear in all the cases, balanced complete bipartite graphs of odd order and the so called odd hatted cycles.
DOI : 10.2298/FIL2304271A
Classification : 05C12
Keywords: Graph distance, transmission of vertex, stepwise transmission irregular graph, eccentricity, Wiener index 
Yaser Alizadeh; Sandi Klavžar. Extremal results on stepwise transmission irregular graphs. Filomat, Tome 37 (2023) no. 4, p. 1271 . doi: 10.2298/FIL2304271A
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     author = {Yaser Alizadeh and Sandi Klav\v{z}ar},
     title = {Extremal results on stepwise transmission irregular graphs},
     journal = {Filomat},
     pages = {1271 },
     year = {2023},
     volume = {37},
     number = {4},
     doi = {10.2298/FIL2304271A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2304271A/}
}
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