Graceful signed graphs: II. The case of signed cycles with connected negative sections
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 1, pp. 25-40
Voir la notice de l'article provenant de la source Czech Digital Mathematics Library
In our earlier paper [9], generalizing the well known notion of graceful graphs, a $(p,m,n)$-signed graph $S$ of order $p$, with $m$ positive edges and $n$ negative edges, is called graceful if there exists an injective function $f$ that assigns to its $p$ vertices integers $0,1,\dots ,q = m+n$ such that when to each edge $uv$ of $S$ one assigns the absolute difference $|f(u) - f(v)|$ the set of integers received by the positive edges of $S$ is $\lbrace 1,2,\dots ,m\rbrace $ and the set of integers received by the negative edges of $S$ is $\lbrace 1,2,\dots ,n\rbrace $. Considering the conjecture therein that all signed cycles $Z_k$, of admissible length $ k \ge 3$ and signed structures, are graceful, we establish in this paper its truth for all possible signed cycles of lengths $ 0,2$ or $3\hspace{4.44443pt}(\@mod \; 4)$ in which the set of negative edges forms a connected subsigraph.
@article{CMJ_2005__55_1_a1,
author = {Acharya, Mukti and Singh, Tarkeshwar},
title = {Graceful signed graphs: {II.} {The} case of signed cycles with connected negative sections},
journal = {Czechoslovak Mathematical Journal},
pages = {25--40},
publisher = {mathdoc},
volume = {55},
number = {1},
year = {2005},
mrnumber = {2121654},
zbl = {1081.05097},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMJ_2005__55_1_a1/}
}
TY - JOUR AU - Acharya, Mukti AU - Singh, Tarkeshwar TI - Graceful signed graphs: II. The case of signed cycles with connected negative sections JO - Czechoslovak Mathematical Journal PY - 2005 SP - 25 EP - 40 VL - 55 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/CMJ_2005__55_1_a1/ LA - en ID - CMJ_2005__55_1_a1 ER -
%0 Journal Article %A Acharya, Mukti %A Singh, Tarkeshwar %T Graceful signed graphs: II. The case of signed cycles with connected negative sections %J Czechoslovak Mathematical Journal %D 2005 %P 25-40 %V 55 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/CMJ_2005__55_1_a1/ %G en %F CMJ_2005__55_1_a1
Acharya, Mukti; Singh, Tarkeshwar. Graceful signed graphs: II. The case of signed cycles with connected negative sections. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 1, pp. 25-40. http://geodesic.mathdoc.fr/item/CMJ_2005__55_1_a1/