Geodesic
On $2$-connected transmission irregular graphs
Diskretnyj analiz i issledovanie operacij, Tome 25 (2018) no. 4, pp. 5-14

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The transmission of a vertex $v$ in a graph is the sum of the distances from $v$ to all other vertices of the graph. In a transmission irregular graph, the transmissions of all vertices are pairwise distinct. It is known that almost all graphs are not transmission irregular. Some infinite family of transmission irregular trees was constructed by Alizadeh and Klavžar [Appl. Math. Comput., 328, 113–118, 2018] and the following problem was formulated: Is there an infinite family of $2$-connected graphs with the property? In this article, we construct an infinite family of $2$-connected transmission irregular graphs. Tab. 2, illustr. 2, bibliogr. 21.
Keywords: graph, transmission irregular graph, Wiener index.
Mots-clés : vertex transmission 
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A. A. Dobrynin. On $2$-connected transmission irregular graphs. Diskretnyj analiz i issledovanie operacij, Tome 25 (2018) no. 4, pp. 5-14. http://geodesic.mathdoc.fr/item/DA_2018_25_4_a0/